Glad to hear you made it to the garage and then home afterwards safe and sound without breakdowns Ellie!
The whistle is probably a combination of the new belt bedding in and the alternator working seriously hard to recharge the battery from its severely discharged state. It might have still started on its own power after the new belt was fitted but would have been fairly well depleted.
See how it goes over the next few days, if my theory is right then the whistle will gradually disappear. I know if i've been doing something where the battery is a bit depleted the alternator does growl/whine a bit (and the belts squeal at the moment too - they need tightening but i'm probably going to renew them instead) until it's recharged the battery.
Hopefully your turbo is in rude health and just needs a service to change the oil/filter to keep it quietly and happily running.
Given the timings though and the obvious extra load on the alternator, my bet is on the new belt bedding in, whining a bit because it's new and working hard coupled with a bit of alternator whine. You've probably not noticed alternator whine before partly because it may not have happened before but mainly because you were likely in a state of heightened awareness where any new (or even not so new) noise is more obvious because you had escaped a breakdown.
The other day for example i renewed the handbrake shoes and disc/drums on the rear. Driving up the road for walkies i heard every pothole i hit with any sort of clonk that i was previously used to ignoring but because i was listening in case something hadn't settled right on the handbrake/shoes/pads etc or even a wheel nut (despite the fact i torqued them twice and then rechecked them) come loose, i noticed every single pothole because of heightened awareness.
See how the whine goes, i'm pretty sure it will disappear over the next few days but if it doesn't then investigate.