@southsamurai@sh.itjust.works did a great job answering your question, I just wanted to add some stats that answer your question more directly:

https://pmc.ncbi.nlm.nih.gov/articles/PMC7984836/

After compiling the results of the update with the previous systematic review, a total of 57 studies pooling 4680 cases were included in the systematic review, and 52 studies were used in the meta-analysis. Overall pooled data including any surgical technique showed rates of 1% [95% confidence interval (CI) <0.1%–2%] of fistula, 11% (95% CI 8%–14%) of stenosis and/or strictures, 4% (95% CI 1%–9%) of tissue necrosis, and 3% (95% CI 1%–4%) of prolapse. Overall satisfaction was 91% (81%–98%). Regret rate was 2% (95% CI <1%–3%). Average neovaginal depth was 9.4 cm (7.9–10.9 cm) for the penile skin inversion and 15.3 cm (13.8–16.7 cm) for the intestinal vaginoplasty.

so, average complications from vaginoplasty include:

• 1% fistula (hole opening up between neovagina and rectum, colon, etc.)
• 11% stenosis (narrowing of the vaginal canal)
• 4% necrosis (tissue death)
• 3% prolapse (inversion and protrusion of the neovagina)

This resource covers the broader range of possibilities, but doesn’t have the rates or stats on how likely they are to occur.

Also remember that complications somewhat depend on the hospital you go to and the surgeon you see, you should be able to ask their specific complication rates, but it is important to do stringent research beforehand to make sure you are going to be in good hands.

There are lots of surgeries trans women can get, and the risks and rates of complications are particular to the surgery.