Intro (v) 0:00-0:06
Verse A 1 0:06-0:41
Verse A 2 0:41-1:16
Middle 8 1:16-1:30
Verse A 3 1:30-2:05
Verse B 1 2:05-235
Transition 2:35-2:40, 2:40-2:45
Verse A & B 2:45-3:09
Coda (trans) 3:09-3:38
Comments: Unlike "Dig a Pony", "I've Got a Feeling" is identical in formal design on both Let it Be and Let it Be ... Naked. The timings are within a second or two of each other (the version on Naked is ever so slightly faster, accounting for the minute discrepancy), so there is little point is listing both. The only significant difference is that the studio chatter at the end of the track on the original album is omitted on the remake.
"I've Got a Feeling" is just the 4th Beatles song so far to use multiple verses in the same song (precedents being  "I Am the Walrus",  "Glass Onion", and  "Julia"). Verse A is clearly dominant over verse B, being heard three times independently compared to verse B which is heard only once independently. In a Beatles first, the two verses are then combined - heard simultaneously - which functions as the structural climax of the song.
The transition is a total of four bars, divided evenly. I am tempted to call some of the transitional material a tag, but it simply is not prominent enough to justify that labeling. Regardless, the coda uses the same chromatic guitar triplets that were used in the transition.