The intention of chapter 23 from Tehillim in connection with Shabbat is the union of Masculine and Feminine (דכרא ונוקבא). This is explained in many Siddurim that include Kabbalistic explanations like for example Siddur Kol Yaacov by Rabbi Yaacov Koppel and Siddur Tefillah m’kol HaShanah by Rabbi Shabbtai of Rashkov.
This is expressed many ways, but one of the easiest to recognize is that there are 45 words preceding the phrase אך טוב וחסד. And 9 words follow the phrase. Thus, אך טוב וחסד, which according to the Ari z"l as discussed in both Sefer Etz Chaim and Sefer Pri Etz Chaim is intended to indicate G-d, is surrounded or enclothed so to speak by the group of 45 words and the group of 9 words.
The 45 words is a siman for masculine as in Adam (אדם which is gematria 45 and alludes to Similar to G-d, Domeh l'Elyon דומה לעליון) and the 9 words are a siman for the feminine because it alludes to the womb which is associated to the letter ט. This reference about ט is mentioned in the Bahir, chapter 124.
In this context, the phrase אך טוב וחסד alludes to what joins the masculine and feminine together. The end letters of אך טוב וחסד are 26 which is a siman for G-d’s name. (In fact, the Ari z"l also points out that the first letters of אך טוב וחסד together with the first letter from the first of the 9 words that are associated with the feminine are also the gematria of 26.)
That the womb, which is associated with the feminine, corresponds to the Makom Panoy (the empty space) that G-d created within His essence in order that the universe (something which on a certain level appears separate from G-d) could be created. And following the explanation in Siddur Kol Yaacov, one of the things we recall on Shabbat is the creation of the universe during the 7 days of Bereshit. That the Makom Panoy is filled with the flow from G-d. This is the words of Kiddush for Shabbat night.
And this points to an underlying theme of Shabbat, namely the 3 partners in marriage (see Kiddushin 30b), איש ואשה, husband and wife together with G-d. Without G-d, יה, all that remains is fire. (אש"י ואש"ה, איש ואשה)