Where does “birthright” come from?

I need to analyze this etymology chain carefully, but I notice there are significant problems with it that make it impossible to write an accurate sentence. The chain shows: - English right → Middle English right → Old French bourde → PIE h₃reǵtós and PIE bʰer- This chain doesn't make linguistic sense. "Right" doesn't derive from Old French "bourde" (which means "jest" or "trick"), and the PIE roots listed don't connect coherently to either word. The repetition of "PIE bʰer-" multiple times and the mixing of unrelated roots (h₃reǵtós vs bʰer-) suggests this chain is corrupted or incorrect. Additionally, "birthright" as a compound would need an etymology showing how "birth" + "right" combined, which isn't reflected here. **I cannot write an accurate one-sentence

birthright (English): Something owed since birth, due to inheritance

Definitions

  1. Something owed since birth, due to inheritance

Ancestry of “birthright”, step by step

birthright traces back through two separate lines of ancestry.

via English birth

StepLanguageWordMeaning
1EnglishbirthThe process of childbearing; the beginning of...
2Middle Englishbirthen
3Old Englishbyrþenburden
4Proto-West Germanicburþiniburden
5Proto-West Germanicburþīburden
6Proto-Germanicburþį̄burden
7Proto-Indo-Europeanbʰēr-shiny, light brown

via English right

StepLanguageWordMeaning
1EnglishrightStraight, not bent; Of an angle, having a size of...
2Middle EnglishrightA good deed, right action; A just or equitable...
3Old Englishrihtstraight; right, true, correct; rightful,...
4Proto-West Germanicrehtstraight; right, correct; morally upright, just
5Proto-Germanicrehtazright, straight; morally upright, just
6Proto-Indo-Europeanh₃reǵtósstraightened, right, upright
7Proto-Indo-Europeanh₃reǵ-to straighten, to right oneself; right; just
Every word from Proto-Indo-European bʰēr-
birthright — Etymology, Origin & Word History | Etymology Explorer