Using DMMs on the mains is somewhat overrated (no pun intended). In a lot of cases it rather akin to beginners getting their first fancy scope, having nothing to look at other than the cal output, and being hypnotically drawn to the nearest mains outlet.
Most use cases are establishing whether mains is present or not, rather than measuring its voltage to within a few volts. Electricians use proper 2-pole testers for such purposes, together with a simple proving unit. These are inevitably at least 600V Cat III. The cheaper professional ones have a basic LED bargraph voltage display, the slightly more expensive ones, an LCD voltage readout too. They normally have a basic continuity and phase rotation tests too, with the same Cat rating. No finger-trouble controls, captive probe lead, and they still give a live voltage indication even if the batteries are flat or missing.
Decent qualtity second hand 2-pole testers can be picked up quite cheaply on ebay (Don't go to Ali!). When you get one, you should carry out the inspections detailed in the manual - check for cracks, lead damage, tug test etc. And verify that they indicate correctly. Proper safe isolation procedure requires indication verification before and after checking the circuit of interest. That's where the battery powered proving unit comes in. You can get those on ebay too, but it's easy enough to make your own with a simple self oscillating inverter - this is pefectly safe to do, if you don't get a reading on the proving unit then any test on the mains circuit is automatically invalid.
Most measurement tests involve a safely isolated, dead circuit. Once the circuit is proven dead and preferably locked off with a clip on the breaker, you can perform resistance measurements etc. Proper second hand insulation and continuity testers (again with the comfort of Cat rating), are again easily available on ebay. They will probably be past their calibration date, but are very easy to verify with a bunch of low and high value resistors and a Cat 1 1kV DMM.
The only other live tests are beyond the capabilities of a DMM anyway. Ze / PSC (prospective fault current) tests require a dedicated tester as does RCD trip current / trip time. RCD testers are also pretty cheaply available too (again they may be past cal, but if an RCD trips at 1 x In and holds at 0.5 x In then it is good enough. RCDs have test buttons anyway.
In summary, there is very little reason to be using a DMM on a live mains circuit.