For a shed office setup, 3 phase is almost certainly overkill unless you're planning to run industrial equipment down the line. Single phase will handle monitors, a kettle, laptop chargers, and general office kit without breaking a sweat.
That said, I'd think carefully about how you're powering it before worrying about phases. If you're anywhere near the shed with decent roof exposure, a small solar setup with a Victron inverter/charger and a decent lithium bank (Fogstar do good value cells) could mean you're barely touching the grid at all for most of the year. That's the route I went with my motorhome setup and the principles translate well to a garden office.
If you do want a grid connection though:
- A decent 32A single phase feed will be more than enough
- Get a sparky to sign it off properly — garden offices can get complicated with Part P
- Factor in an RCD/consumer unit regardless
The kettle is probably your biggest draw at ~3kW, everything else is trivial by comparison. 3 phase starts making sense when you're talking about EV chargers, CNC machines, or serious workshop tools.
What's the rough square footage of the office? And are you thinking fully off-grid, hybrid, or just a straightforward grid spur? Makes a difference to what people would suggest.