Thank you for reaching out and I am happy to assist you with this.
In W3 Total Cache settings, depending on the feature enabled, you can exclude specific pages from being cached.
In Performance>Page Cache>Advanced>” Never Cache following Pages”: add
/cart/and also in
Performance>Minify>Advanced>”Never minify following Pages”:
Once added, make sure to save all settings and purge the cache.
Let me know if this helps!