The battery grip BG-R10 uses the same battery as the camera itself, but two of them. The battery is LP-E6NH, it will also accept earlier versions of the same size battery: LP-E6N and LP-E6. The more recent versions have slightly higher capacity so will be preferable although they're relatively pricey.
Some use third party batteries but Canon have been very much against this, warning of all sorts of problems with these, from lower capacity, shorter useful life, spontaneous combustion (!). Despite this, it's tempting to use them since they're so much cheaper. If you do try a third party battery I would suggest choosing a known, reputable manufacturer from a reliable source who will honour a warranty if it fails.
The only third party battery I have ever tried is the Hahnel Extreme HLX-E6NH battery, which I was given as a freebie by my dealer when I bought my EOS R6mkII. I've used it but haven't yet formed any conclusions regarding its capacity.
The EOS R6mkII consumes power even when it's switched off if Bluetooth is enabled. I haven't tried it yet but there might be less current drain if I put the camera into 'airplane' mode.
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R6mkII, various lenses, speedlites. Also legacy Canons going back to T90 and even A1.
