This seems to correspond to the 'ra_management' option:
- "stateless only" (0: no M-Flag but A-Flag)
- "stateless + stateful" (1: both M and A flags)
- "stateful only" (2: M but not A flag)
So yes, "stateless" actually corresponds to the Router Advertisement flag that allows clients to use SLAAC (with optionally using DHCPv6 Information Requests to get DNS). If you choose "stateful only", clients will be required to use DHCPv6 to acquire an address lease as well.
But note that this isn't something that changes how your DHCPv6 server behaves – it changes information sent in RAs, which tells clients whether and how to interact with the DHCPv6 server in the first place. When stateless mode is allowed (A-flag is set), client devices might not even start DHCPv6 at all – they might be fine with the information already received in RAs.
With that in mind, a big disadvantage of "stateful only" mode is that it will cause issues for clients which don't support DHCPv6. It is possible that currently you have clients (e.g. Android devices) which have no DHCPv6 support and configure themselves entirely through Router Advertisements.
Those clients will no longer have an IPv6 address if you switch to stateful-only mode.
Note that IPv6-Test's website is slightly outdated with its "SLAAC" label. What it really checks there is whether the IP address was generated from your MAC (EUI-48) address, by looking for the ff:fe infix – but that is not actually the only way to use SLAAC anymore.
Modern operating systems will instead use RFC 7217 or a similar scheme to generate their permanent IPv6 address, which is still "SLAAC" but cannot be externally recognized as such.
Temporary addresses (the older "Privacy Extensions") are also assigned using the SLAAC mechanism but with a completely random interface identifier.
