My 2p:
A 1-man tent is hardcore if you have gear that you don’t want to leave outside. My general experience of camping is that comfort is n+1, so if there’s three of you then you need a 4-person tent.
Ultra-lightweight makes sacrifices like “yeah, we didn’t weatherproof it in order to save 12 grams.” Which is more important to you, only you can say.
You can get bike-specific tents which use bits of the bike instead of poles. You are though, obviously, bollocksed if you’re camping when not on the bike unless it comes with optional poles also.
I am undecided on side or front entry.
A long, thin tent should be pitched in-line with any weather you may be having. A front / rear entry will provide shelter from the elements when cooking in a manner which a side-entry may not. Obvs, this doesn’t matter if you don’t get inclement weather, but this is the UK.
Disclaimer, I have never bike-packed. But I have wild camped up hills and done a lot of regular camping. Other posters are likely more experienced than I.