Under IFRS 17, the total liability can be split per Liability for remaining coverage (BEL+RA+CSM) and Liability for incurred claims. So yes, the CSM is a component of the insurance liabilities.
Now, the idea that the CSM offsets changes in the BEL/RA works when these changes relate to future service. For example, if you change lapse assumptions and this results in a BEL+RA increase of 100, the CSM will be reduced by 100 (assuming the CSM before the adjustment was at least 100. If not, loss is recognised immediately in the P&L and CSM set to 0). So in this case the impact on the liability for remaining coverage is indeed 0.
In general, however, the total liability for remaining coverage (BEL+RA+CSM) will change from period to period. Release of profits from BEL will very unlikely match the CSM amortisation pattern. Also, there will be changes in the roll-forward of BEL not unlocked in the CSM at all (e.g. impact of discount rate changes in the general model, expected vs actual variance in claims/expenses incurred in a given period, etc.)