Jamstack low-traffic site: drawing the line between pre-rendered pages and billed serverless functions

I'm planning a low-traffic content site on a Jamstack architecture: pages pre-rendered at build time, served from a CDN, with serverless or edge functions reserved for genuinely dynamic behavior. The goal is to keep monthly cost near the hosting platform's free or lowest tier.

The unresolved decision is where to draw the boundary. Several planned features sit in a gray area: a contact form, site search, and a small members-only section. Each could be implemented as a billed function invocation, handled client-side, or pushed to build time, and the choice changes both the cost profile and the architecture. Build frequency is also a factor, since content updates a few times per week and I'm unsure whether incremental builds or on-demand revalidation are worth the platform lock-in compared with full rebuilds.

Assume a current-generation static hosting platform with metered build minutes, bandwidth, and function invocations; exact limits need checking against current pricing pages.

Which of these features (form, search, gated content) genuinely require server-side functions rather than client-side or build-time handling? How should I estimate invocation volume for a low-traffic site before committing to a platform? Is on-demand revalidation worth the vendor lock-in at this scale?