Can the notice period be negotiable?

I'm a critical resource in a high-stress project as a DevOps Engineer. I used to enjoy working with this team; however, I don’t have a backup, and there are many dependencies on me, making it difficult to take leaves. Even when I’m on leave, they keep calling me.

I’m skilled and have been able to clear interviews, but the 90-day notice period is always a dealbreaker for recruiters, leading to rejections. What should I do? I barely get time to upskill because my project is extremely fast-paced, and the workload drains me. This eventually kills my motivation to learn, making me feel less confident about resigning and applying elsewhere. While there is high demand for my skills in the market, I struggle with self-doubt when it comes to securing a job during my notice period.

I want to switch to a better company. Is there any way to negotiate and reduce my notice period? My manager is toxic and will not let me leave easily, as there is no backup for me and my role has significant dependencies. He won’t even allow me to switch projects if I wanted to.