sRGB mode a necessary for monitors?

The thing is… you don't really calibrate to something specific, unless that's your only ever input and output type. Calibrating to sRGB would mean you could never see outside that gamut - a bit of a waste with a screen that can almost achieve P3.
Let's assume you never (or rarely) need to calibrate for commercial print, which is a whole different ball-game (you can get close with a default setup but your white point would need to be different for a real print-based solution.) Let's stick to photos/videos & predominantly delivery for other computers or via web.

If, for instance, you were to use the X-Rite system with an i1 Display (they make several version of higher quality/greater cost) spectrometer, then aside from setting the software to 'Advanced mode' you pretty much leave everything to the software.
You set to advanced because you can then use the much larger swatch set that isn't available in Basic & really makes a lot of difference to the end result. Leave everything else as it is (Default) right through.
Before you start calibration, it's best to switch your display to a basic 'stupid' mode. Don't let your display try to be 'smart' at all for a calibrated display.
The calibration software will then run you through some basic on-screen settings (brightness, contrast, R,G,B balance) you access through your display's OSD to ensure a 'clean' start point.

What you end up with is an icc profile for your specific display, which is set by the calibration software to be your computer's new default profile. Your computer & software then uses this to translate any input to an output curve correct for your display.

Then, in Photoshop for instance, you check to make sure your display profile is in the list of potential profiles… but you never use it in Photoshop. Your computer is already handling that for you. Photoshop just needs to know it's there.
This is a very common beginner's mistake. People set their Photoshop working profile to their display profile.
This does not work.

You set your workflow to the "best" for your work requirements. Sensible default if you're working predominantly to web/computer is sRGB, but for any already-profiled input, stick with that profile. If you work from a DSLR, then you can use its own profile right the way through. If you need to Export to sRGB, then that's the only time you do. Your input stays at your camera profile - mine, for instance is Nikon Adobe RGB 4.0 - which is "better" than sRGB (wider gamut) but not as good as P3.
Also, my displays can achieve just over 100% Adobe RGB but not P3 so this is a workflow I can use without ever not being able to see the colours as best as possible. If you were using something like a newer iPhone which is capable of P3 for your input photographs, then you'd stay with P3 right through… though as your display can only achieve 95% P3^[1] run a couple of tests first to make sure there are no surprises when exporting to sRGB)

If you work in this wider gamut then reduce to sRGB right at the end - only at export & never change your profile in your PSD document - the difference will become as small as it possibly can be between your intent & what you see on screen after export. Personally, I have real trouble telling the difference between my output JPGs converted to sRGB at 100% quality from my PSDs still at Nikon Adobe RGB.

This, then, makes full use of your screen's capabilities and gives you the highest flexibility at output to whatever your final form must be.

^[1] I did find this review of i1 calibration on your specific display which managed to squeeze full P3 out of it. YMMV - https://www.tftcentral.co.uk/reviews/coolermaster_gm34-cw.htm#calibration