My company is looking for a new SEO agency. What should we look for during our search?

My company is not happy with the SEO agency that we are currently partnered with. Our contract ended back in 2019, and this agency hasn't really provided much for us, outside of content writing (which ranks well but does not give us conversions). I remember tasking them to focus on backlinking and improving page performance, and I recall them being dismissive about it. They just give us the cold impression that they are there to get paid.

Leadership is not happy with them, and frankly, so am I. I've been tasked to explore all options, which includes searching for a new agency to partner with. When looking for a new SEO agency, what are some things that I should be looking for? Sucess stories? Low turnover? Or should we invest in semRush (or something like that) and do it ourselves?

Appreciate the help, and I look forward to hearing the responses!