I wanted to repoint my patio + fix some wobbly slabs. But it turned out a lot of them (23) were actually wobbly and after taking them out, I'm kind of stuck what to actually do. The original mortar was pretty high and applied in "blobs" so I was thinking I should just remove some of it and use the rest as a frame and put new one to it. Or actually should I try to remove as much as possible, use the old mortar as a base and put then something like this over it?
whatever gives the least work for you, chip out so you have 15-20mm of new mortar at the edges, but that might just break free the ones that are hanging on. Then try and give them all a full bed of mortar, but that does require care to get the right level under each one you refit. the dob in the middle, just drive vertically down with a fencing tool like this one: https://www.wickes.co.uk/Wickes-Professional-Solid-Forged-Fencing-Bar---1-8m/p/190344
I am sure they did as good a job on the tamping down as they did with the mortar. It will drive down a bit and give room for some mortar on top. Buy sand and cement separately, it will be much cheaper and with 23 or more to lay you might as well shop around for a jumbo bag of sand, I am sure you will at least use most of it and save repeated trips to a shed.