I also thought that the saber that Obi-Wan gives Luke is the saber that Anakin used for his entire Jedi career.
There’s literally no reason why this shouldn’t be the case in the PT. Like, as much as we disagree with things such as showing Anakin as a child and such, at least there was a specific narrative choice behind that. Not having Anakin use the same lightsaber throughout is just pointless and only serves to take away from the importance of the saber.
Same goes for Obi-Wan (though obviously to a lesser extent because it doesn’t get passed on). I always felt like it could have been a really cool and subtle but powerful thing if, after Obi-Wan lost his lightsaber in TPM, he uses Qui-Gon’s for the rest of his life. Just a little thing, but it could have been easily done and would have given some sense and weight to his changing saber.
Also, what the hell is Obi-Wan doing chiding Anakin about losing his lightsaber in AOTC anyway? Obi-Wan drops or loses his lightsaber more than anyone.