Yes, there is officially—and constitutionally, of course—a clear separation, but traditionally the Orthodox Church has played a very important role. In general, because it's a national Georgian Orthodox Church, there is a tradition of identifying the role of the church and Christianity with a kind of self-identification in Georgia, because of the region where it is located, that it's just Georgians and Armenians who are Christian nations and so on.
In this particular case, and lately, the church has become very closely linked to the government ruling party. It also has traditionally had strong ties with the Russian Orthodox Church. Even though the Georgian Church is independent, the ties are very strong, and it's definitely a conservative force. It has an influence. The patriarch is considered to be a person that many people respect very much, one of the most respected personalities in Georgia, so the position the church takes vis-à-vis certain issues is quite important.
Normally, they are very conservative. They were against anti-discrimination laws, for instance, that Georgia had to pass in order to get visa liberalization with the EU. They are certainly against LGBTQ+ rights.
In this case, they have been relatively balanced but still supportive of the government position.