The Jews prospered in the Middle Ages largely due to their acumen in banking and trade which is why they were valued amongst European Monarchs as they represented a major player in the economic stability of their host country.
The Encyclopaedia Britannica writes:
As European commerce grew in the late Middle Ages, some Jews became prominent in trade, banking, and moneylending, and Jews’ economic and cultural successes tended to arouse the envy of the populace. This economic resentment, allied with traditional religious prejudice, prompted the forced expulsion of Jews from several countries and regions, including England (1290), France (14th century), Germany (1350s), Portugal (1496), Provence (1512), and the Papal States (1569). Intensifying persecution in Spain culminated in 1492 in the forced expulsion of that country’s large and long-established Jewish population. Only Jews who had converted to Christianity were allowed to remain, and those suspected of continuing to practice Judaism faced persecution in the Spanish Inquisition. As a result of these mass expulsions, the centres of Jewish life shifted from western Europe and Germany to Turkey and then to Poland and Russia.
But where they were needed, Jews were tolerated. Living as they did at the margins of society, Jews performed economic functions that were vital to trade and commerce. Because premodern Christianity did not permit moneylending for interest and because Jews generally could not own land, Jews played a vital role as moneylenders and traders. Where they were permitted to participate in the larger society, Jews thrived. During the Middle Ages in Spain, before their expulsion in 1492, Jewish philosophers, physicians, poets, and writers were among the leaders of a rich cultural and intellectual life shared with Muslims and Christians. In collaboration with Arab scholars and thinkers in the tolerant society of Muslim Spain, they were instrumental in transmitting the intellectual heritage of the Classical world to medieval Christendom.
As far as " the Jews being the only ones worthy of dealing with money in these complex ways (related to usury)" - it is largely due to the fact that Usury is something forbidden in the Torah between Jews but not between Jews and non-Jews.
It writes in Vayikra 25:35-37:
If your kinsman, being in straits, comes under your authority, and you hold him as though a resident alien, let him live by your side: do not exact from him advance or accrued interest (I.e., interest deducted in advance, or interest added at the time of repayment.), but fear your God. Let him live by your side as your kinsman. Do not lend him your money at advance interest, or give him your food at accrued interest.
This is codified in Halacha. Rambam in his Mishneh Torah, in Malveh VeLoveh (Lenders and Borrowers) 4:2 writes:
Just as it is forbidden to give a loan at interest; so, too, it is forbidden to borrow at interest, as Deuteronomy, ibid., states: "Do not offer interest to your brother." According to the Oral Tradition, we learned that this is a warning to the borrower.
Similarly, it is forbidden to act as a broker between the borrower and the lender when interest is involved. Anyone involved, a guarantor, a scribe or a witness transgresses a negative commandment, as Exodus 22:24 states: "Do not lay interest upon him." This is a warning against the witnesses, the guarantor and the scribe.
Thus, we see that a person who offers a loan at interest violates six prohibitions:
"Do not act like a creditor toward him," "Do not give him your money with neshech" "Do not put forth your food at marbit" "Do not take neshech and tarbit from him" (Leviticus 25:36), "Do not lay interest upon him," and "Do not place a stumbling block in front of the blind" (Leviticus 19:14).
A person who borrows at interest violates two prohibitions: "Do not offer interest to your brother." "Do not place a stumbling block in front of the blind"
The guarantor, the witnesses and the like violate only the prohibition: "Do not lay interest upon him." Any broker who connects between the lender and the borrower or assists or instructs one of them with regard to making the loan transgresses the commandment: "Do not place a stumbling block in front of the blind" (Touger translation)
Now although the issur of ribbis (usury) exists only between Jews it is worth noting the Gemara in Bava Metziah 70b which notes:
Rav Naḥman said: Rav Huna said to me that this verse is necessary only to state that even interest that a Jew took from a gentile will ultimately reach the government treasury, and the one who took it will not be successful. Rava raised an objection to the statement of Rav Naḥman: The verse states: “Unto a gentile tashikh” (Deuteronomy 23:21), which indicates that it is permitted for a Jew to take interest from a gentile, as what is the meaning of “tashikh”? Doesn’t it mean the same as tishokh, take interest, thereby teaching that one may take interest from a gentile? The Gemara refutes this claim: No, it means to pay interest, meaning that you must pay him interest. (Sefaria translation and notation)
Tosafos on this piece develops this idea of "tashikh" and mentions a point that it is pertinent to your question. The noteworthy excerpt reads as follows:
ולא אסרו מעולם רב נחמן ורב הונא רבית דנכרי ואפי' ללישנא קמא יש להתיר לפי שיש עלינו מס מלך ושרים והכל הוי כדי חיינו ועוד שאנו שרויין בין האומות ואי אפשר לנו להשתכר בשום דבר אם לא נישא וניתן עמהם הלכך אין לאסור רבית שמא ילמוד ממעשיו יותר משאר משא ומתן
And Rav Nachman and Rav Hunah don't ever forbid usury with a gentile, and even according to the first teaching one can permit it since there is on us (Jews) tax from the king and officers and all of it is part of our lives. Furthermore, we are permitted to charge interest amongst the nations (i.e. non-Jews) and it is impossible for us to earn wages (i.e. subsist) unless we maintain business with them. Therefore we don't need to forbid usury since perhaps he will learn from his actions more than any other business.
So with this Tosafos in mind, we see that Jews are allowed to deal in moneylending etc. especially when it is their main means of subsistence. The fact that they were proficient in trade and banking etc coupled with the point already mentioned that Christianity did not allow moneylending for interest meant that they were well placed to take the lead on the European stage, thereby making them a powerful player on the economic grand scale which allowed them to forge important connections with monarchs and other European leaders.
As far as the Radhanites that you mention, they dominated the trade routes throughout the medieval period which is why they enjoyed the good relationship with European monarchs as they controlled much of the economic development of the period.
There is a fascinating website here which writes:
The Radhanite Jewish trade routes prospered from roughly 750 to the late 800’s. Almost all key scholars agree that for more than a century, “virtually every drop of spice that entered Europe did so through the hands of the Radhanite Jews”, as they held the monopoly on spices, slaves, and luxury goods. One of the biggest sources of income for the Radhanites was mediating between East and West, between Christendom and Islam, and between the Kings, Caliphs, and Khagans, who all engaged in enslavement of tribes and peoples. Radhanite Jews came to dominate all early medieval trade routes and river systems, and gained a virtual monopoly on the transit of slaves , which they took with them throughout the world.