Core Web Vitals definitely should be your priority and be at the core of your performance strategy however it is worth also checking out the other Web Vitals. These include:

Speed Index

TTFB (Server Response Time)

First CPU Idle

First Meaningful Paint

TBT (Total Blocking Time)

Web Vitals will evolve and develop over time so it is definitely worth being prepared and optimising your site as frequently as possible. There is definitely no quick fix and this will be an ongoing project through keeping an eye on industry developments and putting Customer Experience at the forefront of your strategy.