A direct invite that arrives while the gateway is running fires
_on_invite, which passes is_direct and the inviter through
_schedule_invite_join so the room is recorded in m.direct after the
join. An invite that is still pending across a gateway restart takes a
different path: _schedule_pending_invite_joins reconciles it from
rooms.invite in the sync response, but called _schedule_invite_join
without is_direct or inviter. The DM signal was dropped, the room was
never recorded in m.direct, and it was classified as a group until the
user's own client happened to update m.direct.
Read the signal from the stripped invite state instead: the
m.room.member event for our own user carries the original invite's
is_direct flag, and its sender is the inviter. Thread both through to
_schedule_invite_join so a reconciled direct invite is recorded in
m.direct, and thus lands in _dm_rooms, exactly like a live one.
This gap was surfaced by the triage of #62493.
0ce3e7b12b