As has been pointed out before, there really isn't any urgency for either team to do anything... the most likely outcome is that nothing at all happens.
Aiyuk can do the soft holdout as long as the 9ers let him, but he really is at their mercy. The CBA is brutal on holdouts under contract... especially for first contracts... they could force him to play under the 5th year option and his only other option is to retire...
The 9ers want him playing for them. They are SB contenders and have little use for picks unless they can flip them for other players. They are trying to keep him pacified until he decides to play for them.
The Steelers aren't by any report, desperate for WR help. They believe they will be ok if everything holds the way it is, but they are open to a long term upgrade if its not outlandish in cost. Since they didn't blow the 9ers away with an offer, there isn't going to be any quick resolution... if Aiyuk decides not to sign an extension, this could linger until the deadline.
They only three ways this goes through..
Aiyuk burns bridges in SF,
A third team is willing to flip the compensation the Steelers are giving up into players the 9ers need now.
An injury to a steelers wr creates a bigger need and they up their offer...