If your interpretation were correct then there could be no regulation of assembly at all. This is not correct and SCOTUS has already supported content-neutral

If your interpretation were correct then there could be no regulation of assembly at all. This is not correct and SCOTUS has already supported content-neutral time/place/manner restrictions on assembly, for more than a century iirc. Saying "no gatherings of more than 1000" is facially legal. Plenty of protests have been told it's time to disperse before. Furthermore, SCOTUS typically grants even wider powers in extigent circumstances. It is probably also legal to say "no gatherings at all, everyone back to your houses for the duration of this crisis". An example would be something like the boston bomber crisis, although I don't think it was litigated, that probably would have been found to be legal as well.