Dear Dr. Konôpka, dear Prof. Hutter,
thank you very much for the helpful hints! After additional tests with the plane wave Sirius implementation, I could find the following answers:
1) In the case of pure S the problem was really in the basis. So with Sirius, it was possible to get an immediate agreement. When I picked TZV2PX, I got the agreement with Quickstep too.
2) In the case of MoS2, where I initially checked the convergence of the basis, it turned out to have no significant impact.
However, in further tests I noticed a difference in the electrostatic energies. To reproduce the results from CP2K in CPMD, it turned out to be necessary to increase the number of additional supercells included in the real space sum for the Ewald term (the TESR was zero by default).
Best regards,
Nikita