Flopping salvia is a very common problem. It tends to happen more if the plant is not getting enough sun, or is getting more fertilizer than it needs (it doesn't need much, so in rich garden beds it is too much).

You could try cutting it back to lighten the stems and get some rebloom, but I always have to resort to some sort of staking or other form of support to keep it from flopping over. Peony rings and short, wire garden fencing is what I typically use. You could also consider replacing it with other spiky but less floppy plants, like Veronica.

P TW - Thank you so much for the advice! I will look for something to support it, that's a good idea.