cheap but good vacuum cleaner?

Get a canister with bags, bagless vacuums spread fine dust everywhere because their cheap undersized filters leak. From previous research the eureka mighty mite is the most recommended cheap vacuum on reddit if you're in North America. If you have wall to wall carpet you may want something more powerful, but you at least will want a turbo brush head (where the vacuum power runs the brush head instead of a separate motor). If you only have hard floors the standard heads are fine.

I went the bifl route and ended up with a Henry due to it's modular repairable/rugged design and good air filtration system.

If you want cheap and good suction it has to be bagged

The Project Farm youtube channel has done some good head-to-head tests https://www.youtube.com/@ProjectFarm/search?query=vacuum

Mouth

no idea but a shitty Amazon bagless one came with my flat and although the suction wasn't great, I really liked the convenience and no-cost of no bags. Could be a feature to consider.

what kind of floors do you have?

if bare or very low pile carpet (like, berber might be pushing it kinda low-low) this little guy is pretty nice. very maneuverable and lightweight, the quick-detach head thing gets regular use, super easy to dump it in the trash. it cleans better if you dump it after every room, but when I'm feeling lazy, I'll do the whole house in one go and it's fine.

the reviews mention it doesn't do carpet well at all which I totally believe, there's some berber in one area that it struggles to clean, but I can drag the shopvac to the berber when it really needs it

are you handy? there might be after-market parts for your Dyson

I have a Xiaomi vacuum cleaner, still expensive but way cheaper than Dyson, and quality is definitely there

Uhhh I dunno, Zelmer seems fine to me