Welcome Gavadava,
Apologies for not chipping in on this, but partial house demolition and foundation excavation have been dominating life for the past few days.
So far as I am aware there shouldn't be any excessive backlash between the clutch drum gear and the drive gear on the end of the crankshaft. I can find no specific clearances in either the Yamaha SRX600 workshop manual or my Clymer XT600 workshop manual; I use the latter as a cross-reference at times, because it has clearer illustrations.
If you have excessive backlash between these gears, I would suspect that the either the engine has been mercilessly 'plonked' in too higher gear; or that the nut holding the drive gear onto the end of the crankshaft was not torqued sufficiently; this has slackened and allowed the gear to slacken and try to shear the key in the keyway in the crankshaft, so allowing the excessive backlash to develop between the drive gear and the clutch. The clutch drum is on a splined shaft and I think it unlikely that this will be where the backlash is coming from.
You maybe fortunate enough to only require a new key.

However, if the keyway has been enlarged in the crankshaft this will prove expensive, but not insurmountable!

If you would like a copy of the Yamaha SRX600 manual in pdf, drop me a 'Personnel Message' using the link beneath my avatar on the left of the post, with your email address and I will forward you a copy via 'WeTransfer' (cloud data transfer) so as not to clog up your emails with a large file.
If you would prefer to speak to an experienced professional, then Martin Sweet at Slipstream Tuning is worth contacting. Google "Slipstream Tuning" or if you use 'Facebook' contact them via their page there. 35 years experience of these motors in all forms from Supermono to Paris-Dakar and 'Standard'.
Building may delay my reply, but SteveL and or SteveH maybe along to either corroborate my thoughts or offer others of their own and try to guide you.
For technical diagrams/parts lists/ordering, the Fowler's website takes a lot of beating. Alternative parts maybe available from other suppliers, but quality may not be the same and with these parts of the engine, Yamaha original are usually the best.
Fowler's parts link:
Fowler's_PartsI hope this helps.
My regards, Bill