Spyre brakes work just fine and will stop you.
5800 calipers with 4600 shifter work just fine and will stop you.
Yes there is a different pull ratio on the caliper brakes. No it wont cause any actual safety issues as the difference is quite minimal. If you are concerned though, just buy some matching brake calipers that are the same pull as your shifters- older Tiagra, 105, or Ultegra would work.
Also, the T in TRP stands for Tektro. TRP is a division of Tektro. Tektro brakes can be of low quality and can be quite nice since they sell a full line of options.
TRP caliper brakes can be quite nice- I chose them instead of Shimano for a recent build.
Tektro, promax, origin8, shimano, XLC - these can all work just fine or be crummy. It heavily depends on if you have good pads and if they are set up properly. Even cheap dual pivot brakes work fine with good pads and proper setup.
Buy the bike that fits best, then address the brakes if that's even needed.