Turkey is an ally of Russia and Iran in Syria hence on the side of the current regime.
That’s a very long way from the truth. Until fairly recently Turkey was actively opposed to Iran and the Assad regime for 2 main reasons: one, the extension of Iranian (Shi’a) influence westwards stymies Erdogan’s aim of reestablishing an Ottoman-style (Sunni) influence over the region. Two, more pressingly the Assad regime tolerated the presence of the Kurdish groups with which Turkey has long been obsessed. Turkey’s active opposition to the Assad regime has been suspended in response to 2 short-term factors only: one, a desire to avoid friction with Russia (certainly falling short of an alliance, evidenced by continued US and UK access to Turkish airspace) and two, the current inability of the Assad regime to do anything to prevent Turkey’s new Kurd-suppressing activities in northern Syria. As and when these short-term factors subside, the strategic reasons for Erdogan to oppose Assad will reassert themselves. I can’t see him being anything but happy for the West to chip away at what is essentially Iranian power.
It’s true that there are risks to using Akrotiri as a base for striking Syria, but not from Turkey IMHO. I would be far more worried about what political trouble the Russians could stir up in the RoC. I can’t see them attacking but some ‘threatening’ westbound sortie profiles out of Syria would quickly stir up a hornet’s nest.