I know this sounds unhelpful, but it mostly depends on what exactly you want to start with. However, you will absolutely need a multimeter, no matter what you do. Expensive brand name multimeters are great and I have a few. But for starting out I would get a cheap auto ranging meter in the 20-50 $/€ range. Maybe an Aneng or Zoyi or some such. They are certainly good enough for most electronics needs, unless you are working on higher power/voltage/current. If you have the money, something from Brymen or a similar brand is nicer but not required. If after a year or two, it turns out that you really love electronics and feel the need for a better meter, you can get a more expensive one when the need arises and the cheap meter is still useful because you want two meters in the long run, anyway.
Do you need a lab psu? And what kind? This one heavily depends on the nature of your projects. Arduino/ESP etc. – a cheap wal-wart is enough. Analog electronics – probably a linear PSU. Driving motors – PSU with lots of power, probably a switcher.
Soldering: do yourself a favor and get a soldering station. It does not have to be fancy. They are not that expensive and the fun to price ratio is so much higher than with a simple iron. Some people love the USB-irons and most of them certainly work well, but I only use them when on the go (repair cafe) because I don't like the shape of the handles and cable flexibility very much. Also get decent solder wire and flux.
If you want to do microcontroller/digital things, get a cheap logic analyzer – it will open our eyes about the things going on between the chips. Even the cheap ones are more handy than the logic part of most digital scopes.
An oscilloscope is a very nice thing to have for anything analog and to some extent also digital. Don't buy crap like the FNIRSI thing. If you can afford it, something like the Siglent SDS804X HD is great. If you don't have that kind of money, try to find a bargain used Siglent, Rigol or similar for the start and keep saving until you can afford a decent new one. I also like old analog scopes that sometimes can be found cheap, but I'm not so sure if I'd recommend that to a beginner, as they can be pretty intimidating at first.
Some kind of signal source is very useful. Even cheap signal generators go a long way. For the start, that may even be our PC soundcard or a phone app plus an adapter.
Hand tools: small side cutters, screwdrivers, needle nose pliers, wire strippers (automatic are best).
Anything else: buy it when you need it, not because you may need it eventually. Tool collecting is a hobby in and of itself, but if you are on a budget, don't get into that. Any time that happens, feel free to ask for recommendations here.