Personally, if I'm doing intervals, I don't stop my watch in between. Mostly this is so my Garmin-recorded PB doesn't automatically update. I don't want it telling me I beat my 5k PB because I did 12×400 m in 90 sec, ignoring the 60 sec rest between each.

But it's also so the overall activity pace doesn't look deceptively fast to friends on Strava. And it's also so that I can use the "lap time" of my rest "lap" (I hit the lap button manually, when doing intervals, rather than using the automatic 1 km laps) to time how long my rest should be.

Delete the activity already recorded? No, I wouldn't. If you've broken any PBs, I'd go in and manually revert those, and maybe add a description to the activity explaining that it was intervals.

I do pause my watch, without shame, on my longer runs, when I'm stopping for water, or to cross the road at lights.

If it is cheating, you're only cheating yourself

It doesn't matter to me. If it bothers you, then delete it. The only person that really cares about your stats is you, so do whatever keeps your conscience clear.

In many areas of my life I used to be very strict with these kinds of problems, but I have learned recently that it is a lot of expended worry and energy about what ultimately is an insignificant difference.

I try to tolerate minor margins of error like this now, because I think it makes me happier and more relaxed, and that is ultimately more important to me than having a slightly more accurate record.

you could use it as motivation. i got a similar 10k pb not long after i brgan running by pausing, resting and running again. realised a few years later it was probably not the most accurate and went out and smashed it.

Personally I wouldn't have paused the activity. Instead I would have used laps to mark the start and end of each interval.

Since you said it's close to your pb and not an actual new pb, I wouldn't bother deleting it. I just wouldn't want a 5k pb to be from anything other than actually running 5k straight.