Does my old villa need a distribution-board upgrade before I add more load?

Three of the things you just described each independently justify an upgrade, so together it's a clear yes.

The rule I use: a distribution board needs upgrading (not just filling) when any of these is true — it's out of spare ways for the loads you actually need, circuits aren't protected by a working RCD, or it's unlabelled/overcrowded/showing heat. You've got all three. Squeezing an EV charger and a pool pump — both big continuous loads — into a full, partly-unprotected 12-year-old board is exactly how you get nuisance trips at best and an overheating board at worst.

What a proper DB upgrade involves: the electrician specs a new board with enough ways for your current and planned circuits, proper RCD protection grouped sensibly (so one fault doesn't kill the whole house), re-terminates and labels every circuit, and tests earthing and each breaker. It's usually a half-day to a day with a planned power-off, not a week — but it's licensed work, full stop, never a handyman job.

Do it in the right order: upgrade the board first, *then* add the EV charger, pool pump and new circuits onto a board built to carry them. Adding the loads first and upgrading later means paying twice. Given the unlabelled board and missing protection, I'd also treat this as overdue on safety grounds — get a licensed electrician to assess and upgrade the board, ideally alongside the safety inspection you were already thinking about.