This. Don't take it for granted that a spirit level or a sheet of metal is flat just because it looks that way.
Interestingly, I found flatness not in my DIY toolbox but in the kitchen. If you take a piece of quartz countertop, you can expect 1/32" in 8 ft of tolerance (0.3 mm in 1 m) or even 0.0001"/foot (0.008 mm in 1 m) depending on grade/finish. This is because customers want a nice accurate clear reflection (instead of float glass-like distortions) and definitely don't want lippage (which you get when two panels are not precision flat).
Check with your local stone mason if they have any piece of scrap engineered stone you could take. Polished granite or quartz surface are other names it may go by. They should be happy to get rid of scrap. Ideally, they'd cut it for you too, but that's less likely to happen for free. If you get hold of a nice piece sufficiently big for fret levelling and decide to cut it yourself, seek guidance. Please please DO NOT use a dry grinder blade. It'll shatter and may hurt you in the process. Wet cut only.
Re DIY tools in general, you'll find a lot of information on youtube, for example: