It’s actually something that is changing in English right now. In some languages like German all word-initial vowel sounds are pronounced with a glottal stop at the start (a so-called “hard attack”) but English generally doesn’t (or didn’t) do that, resulting in “thee apple”. Younger speakers are starting to use hard attack before word-initial vowel sounds so the “thee” variant isn’t present for them.

I’m not sure if this also affects “a” vs “an” (i.e. I don’t know if younger people are starting to say e.g. “a apple”) because that obviously makes an orthographical difference so it might be more persistent. Although I suppose they coud say both “an” and begin the next word with a glottal stop.

Keep an ear out if you’re listening to a younger native English speaker and you might be able to hear it.

British English speaker: for me, the two 'e's' have the same sound.

The boy The apple.

Though I do say 'thee end'

My Brother says 'barth', I say 'bath'.

Also native British. I would say "thee apple" would be by far the more common pronunciation in op's example but I probably wouldn't blink if someone said "thuh apple".

Yeah, these are different for me as a southern Englishman. Languages generally try to avoid glottal stops. French has a lovely system called liaison where a consonant sound will appear to separate two consecutive vowels. In English we like diphthongs so I guess we use this similarly to liaison. Some accents just use glottal stops, though, nay bother.

Both schwa for me, native speaker who grew up in Scotland.

Australian native speaker here. Only the first "the" is a schwa for me.

Must be tied to how we both pronounce the first "a" in apple differently.

Both schwa for me unless I was trying to draw particular attention to the apple and denote it was rather significant.