Is it halachically permitted for one to eat pure meat, i.e. turkey, lamb, etc. even though it wasn’t killed in a kosher manner (Kashrut)? For example, store bought turkey breast.
No it is not permitted.
הָאוֹכֵל כְּזַיִת מִבְּשַׂר בְּהֵמָה שֶׁמֵּתָה אוֹ חַיָּה שֶׁמֵּתָה אוֹ עוֹף שֶׁמֵּת לוֹקֶה שֶׁנֶּאֱמַר (דברים יד כא) "לֹא תֹאכְלוּ כָל נְבֵלָה". וְכָל שֶׁלֹּא נִשְׁחֲטָה כָּרָאוּי הֲרֵי זוֹ מֵתָה.
A person who partakes of an olive-sized portion of a domesticated animal, wild beast, or fowl which dies is liable for lashes, as [Deuteronomy 14:21] states: "Do not partake of any nevelah." All animals that were not slaughtered in the appropriate manner are considered as if they died.
(Translation by Eliyahu Touger)
The laws of Kashrut (for Jews) require that the animal be killed specifically by kosher slaughter. This applies to both mammals and birds.
A kosher species killed any other way – or one that died on its own – is called a neveilah and is prohibited.
לֹ֣א תֹאכְל֣וּ כׇל־נְ֠בֵלָ֠ה לַגֵּ֨ר אֲשֶׁר־בִּשְׁעָרֶ֜יךָ תִּתְּנֶ֣נָּה וַאֲכָלָ֗הּ א֤וֹ מָכֹר֙ לְנׇכְרִ֔י Don't eat any unslaughtered animal; gift it to your local visitor and they can eat it, or sell it to the foreigner.
There are many people who think kosher is just about the species, but how it was killed matters too.
The theoretical punishment for eating, say, rabbit meat is the same as eating turkey that was killed by anything other than kosher slaughter. (I know the comments here will get into some very theoretical nitty-gritty distinctions, but ...)