The warlock's Pact Magic feature says:
The Warlock table shows how many spell slots you have. The table also shows what the level of those slots is; all of your spell slots are the same level. To cast one of your warlock spells of 1st level or higher, you must expend a spell slot. You regain all expended spell slots when you finish a short or long rest.
If you multiclass from another caster class and take a level in Warlock, do all your other spell slots suddenly start recharging over a short rest?