The other answer is glossing over the shift over time in Turkey's approach to the matter. There's good background article on the more recent approach in the New York Review of Books. Basically, Turkey has assumed more direct control of their proxies in recent years. Some excerpts:
The creation of the Turkish-backed Free Syrian Army (TFSA), also known as the Syrian National Army (SNA), was the result of a strategic shift in Turkey’s position in Syria. In the early years of the civil war, Turkey aimed to remove Assad from power. Following Russia’s direct intervention in the war, in September 2015, the balance of power decisively shifted in favor of the Assad regime. Turkey therefore adjusted its ambitions to advance a narrower set of interests. At the top of Ankara’s priorities were the aim of preventing the entry of additional Syrian refugees and a desire to combat the Kurdish People’s Protection Units (YPG) [...]
But who exactly are the roughly 35,000 Syrian men fighting on Turkey’s behalf in Syria? I have maintained regular contact with some of these fighters since as early as 2014. Most are Sunni Arabs, displaced from their homes in the course of the war. Multiple interviews I have conducted by phone, instant-messaging, and face to face in Turkey with these fighters since 2014 reveal them to be a motley crew of often traumatized and impoverished men who feel pushed into fighting on Turkey’s behalf for financial gain. Some of these fighters join the factions to rob and loot, but those who did not have that motive increasingly realize that Turkey’s interests do not align with their hopes of toppling the Assad regime, as Ankara signals its willingness to cooperate with the Assad regime. Individuals like this, I have found, struggle to rationalize and justify—to themselves and their communities—their actions and affiliation with these factions, which are much-despised by fellow Syrians, particularly by civilians living under their rule. [...]
Except for a few skirmishes, the Turkish-backed factions have not fought the Assad regime. All three operations carried out by Turkey involved “de-confliction” arrangements with Russia (and, by extension, the Assad regime) before they began. These arrangements continue: the areas under SNA control are not bombed by the Assad regime or Russia, unlike rebel-held areas. [...]
Side-note: there have been some exceptions to this more recently. But back to background story:
Turkey maintains authority over its proxy in the use of force in military action. The fighters’ salaries, training, and supervision in battle are also provided by Turkey. Speaking from a checkpoint he was manning in Tel Abyad, a town captured from Kurdish-led forces in the latest SNA offensive, a fighter with an SNA faction named Faylaq al-Majd from Idlib whom I will call Muhammad (the names of all Syrian subjects in this article have been changed to protect them from possible reprisal) explained “the fighters here are like donkeys, following their masters. And the commanders are also donkeys, following Turkish orders and even if this harms the interests of the [anti-Assad] revolution, they don’t care.”
“All decisions, big and small, in the ‘National Army’ are made by the operations room run by Turkish intelligence,” confirmed Mazen, a veteran rebel from Rastan, in the northern Homs countryside, now fighting in the ranks of the Levant Front, another SNA faction. He was echoing all my interviewees in admitting that decision-making was out of the hands of the Syrian commanders themselves. Mazen underwent training by Turkish military personnel in Turkey and Syria.
The Turkish-backed fighters are a mix of former rebels and newly recruited fighters. Turkey relied on already existing Syrian rebel factions, some of which once received support from the CIA-led Military Operations Command or the Department of Defense Train and Equip Program. The CIA-run program, codenamed Timber Sycamore, was shut down in late 2017, while the Train and Equip Program in northwestern Syria failed back in 2015. Among the groups that once received US-directed support were Levant Front and the Hamza Brigade (which later merged with other rebel groups to form the Hamza Division). Turkey took over the payment of salaries to the fighters prior to the 2016 operation and significantly augmented their ranks. The factions grew in size, from dozens and hundreds of fighters to thousands. The largest rebel groups incorporated into the SNA, the factions that make up Ahrar al-Sharqiya and Jaysh al-Islam, did not enjoy Western support. [...]
The Wikipedia article on the latter group (citing almost exclusively pre-2016 sources) still says they are backed by the Saudis, which is probably no longer the case much.
The majority of the fighters today appear to be newer recruits, without any previous experience fighting the Assad regime. The fighters and commanders in the ranks of the SNA interviewed for the article estimated that the fighters who enlisted into the ranks of the factions for the 2016 operation, and then in another recruitment drive before the 2018 Efrîn invasion, make up 60 percent of the force. These fighters—known, ironically, as “the 2016 revolutionaries”—“mostly joined for the salaries, not for the revolution,” said Mustafa, a commander in the Hamza Brigade, who had himself joined the Syrian armed opposition in 2013, at the age of fourteen.
Besides paying the SNA (decreasing salaries), Turkey also pays for the administration in the areas the SNA nominally controls:
The governance of areas under SNA control in northern Aleppo and in the newly captured areas in northern Raqqa and Hassakeh is closely tied to Turkey. Turkey pays the salaries of local councilors, teachers, and doctors, in addition to the salaries of the local police, military police, and armed factions.
So as you can hopefully see, Turkey nowadays is much less interested in supporting groups that have other goals than doing Turkey's bidding, so the SNA and the areas they control are more or less a puppet of Turkey with little in the way of overt political goals they can pursue.
