Do I need Minecraft 1.21.10 installed to join?

Usually, yes. If a server lists 1.21.10, expect it to require that client. Some networks use cross-version bridging, but it can introduce subtle issues like mismatched hit feel, weird block interactions, or item and UI desync.

Why would a server stick to 1.21.10 instead of updating immediately?

To keep a stable target for plugins, datapacks, and balance. It reduces update-day breakage and protects long-term projects where small mechanical changes can invalidate farms, builds, or competitive setups.

Does being on 1.21.10 guarantee my farms and redstone will work the same everywhere?

It helps, but it is not a promise. Simulation distance, mob caps, random tick speed, and performance plugins can change rates and reliability even on the same version. Technical-focused servers usually publish those settings.

Is Minecraft 1.21.10 only relevant for vanilla survival?

No. SMP, factions, and minigames all benefit from a pinned version. The point is that the server experience is built and verified against 1.21.10, so the intended mechanics are consistent.