Budget is upto a 100.

Nice small bag that won’t sit on my lower back.
Doesnt need to be bike specific ’cause I don’t use bladders.

What’s good?

what volume?

I have an old deuter race air with the suspended rear brace which stops sweat soaking of the bag, but is only 15L – I use it as a day bag or ride bag. Mrs S has the larger 20L version.

My favourite bag is probably my 45L Lowe Alpine bivvy rucksack. But it has a padded back so I sweat into the padding.

TBH I dont think there’s much that will stop you sweating, the right base layers/layers are more important for dealing with sweat than the kit.

I converted to the mesh back suspension system back packs many moons ago, after using a CB mule for a summer, and won’t be changing back. Doesn’t stop you sweating and getting a damp t-shirt but it does stop you putting on a nasty wet backpack mid-ride/post stop & the gap does allow for some ventilation to dry your t-shirt out as you ride. Not sure how you going to avoid any ruckpack sitting against your lower back though.
Vaude, Deuter, Osprey & Berghaus (& no doubt others) make rucksacks with suspension systems, pick one that fits your sizing needs.

How about a waist pack?

Let’s call it a bumbag fannypack and be done with it.

I experimented with them but didn’t like things on my waist.

Base layers are all high wicking/ good quality.

15l would be enough: water bottle, snack, spares. Mostly for 4hr rides that start and end at home.

If you have a Decathlon nearby they are worth a look.
on line here
I have an older 30ish litre light sack that copes well, though I haven’t biked with it.

Have you thought about a frame bag or something?

Berghaus Freeflow 20, perfect for big days out, the bag is miles from your back, even the straps are ventilated. Waist strap isn’t amazing so does tend to slip up a bit on really steep stuff when its heavily loaded.

Deuter Race Air stays off the back and keeps me dry on and off the road.