I'm looking to buy some speedlights/strobes but I really do not want to buy all new transmitters and receivers when I have the Yongnuo set.

Then stick with Canon RT-compatible gear.

Will any strobes/speedlights from the Godox series be compatible ?

No, not if you want any more control over the strobes/single-pin manual speedlights than remote firing. With the TTL speedlights, you'd need to add YN-E3-RX receivers to the feet. The built-in radio triggering is only compatible with Godox transmitters.

Radio systems of different brands are incompatible (with the exception of the FusionTLC Raven), and Yongnuo themselves make four separate incompatible radio triggering systems. [Well, strictly speaking, five systems, since they added the YN685EX-RF/YN32-TX for Sony...]

... If not, what is compatible with the Yongnuo [transmitter] other than the Yongnuo YN200.

Actually the YN200 is not compatible with the YN-E3-RT. It's only compatible with the YN-560-TX Pro (and not the YN-622-TX; you can supposedly fire and M power control it with a YN-560-TX [non-pro] but not use TTL or HSS). Yongnuo was supposed to unify the 622 TTL and 560 manual triggering systems with the YN-560-TX Pro and firmware updates, but they never made firmware releases for the 622 gear available.

The YN-E3-RT is Yongnuo's clone of Canon's ST-E3-RT transmitter. It works well with any of Yongnuo's or Canon's RT speedlights. Theoretically, it should also work with Westcott FJ/Jinbei RT gear (FJ80/HD2-Pro; FJ200/HD200 Pro; FJ400/HD400 Pro) which are also RT compatible, but reports are that Yongnuo's RT reverse-engineering doesn't work with Jinbei's RT reverse-engineering. The only other directly RT-compatible strobe I know of is the Phottix Indra500LC monolight. No idea if it works with the Yongnuo RT gear, either.

If you want to get Godox lights, you're going to have to get a $60-$70 Godox transmitter to go with them. The main reasons most of us switched to Godox from Yongnuo is because Godox has a single unified 2.4 GHz radio system where the $60 TT600 works alongside the TTL/HSS TT685; supports not just Canon and Nikon TTL/HSS but also TTL/HSS for Fuji, Sony, MFT, and Pentax and that support is cross-brand; all the speedlights in the system are equipped with built-in radio transceivers; and there are multiple choices for bigger-than-speedlight options (like the AD200).

Yongnuo dead-ends you relatively quickly in expansion terms if you decide to stick with them; Godox doesn't. Hopefully in the future we can say the same about the Westcott FJ/Jinbei RT system.