If you don’t currently have a bike, there’s no problem with starting out with just 1 bike. The Jamis sounds like plenty of bike for going on group rides etc whilst also being entirely appropriate for commuting (people ride Sora bikes to work every day).

It’s a shame the Felt might not work out, as 10 speed DuraAce would be my choice over any Sora group, particularly if it’s the old thumb-shifter Sora.

I wouldn’t deliberately go out and get a clunker like the Technium unless it will genuinely clear up enough budget for you to then get a good, lightweight, modern, newish true road bike.