The only wireless masters that will work with a YN-565EX III's built-in triggering capabilities (Sc mode) are masters in Canon's "smart" optical system: the pop-up flash in a 600D or higher/later model of body that has one; or another Canon speedlight with smart optical master capability that works on a 2000D (e.g, Canon 580EX II, Canon 600EX-RT, or Godox TT685C firmware updated for 2000D compatibility). Unfortunately, the 2000D's pop-up flash does not have master capability.

The "dumb" S1/S2 modes can be triggered by any flash burst (so the 2000D's pop-up flash could be used for this), but will only fire the flash. TTL, HSS, group, power, and zoom remote control are not possible. S1 fires on the first burst sensed, S2 on the second to avoid firing the flash early from a TTL metering pre-burst.

Optical works great in studio conditions with low ambient levels and lots of bounce surfaces around to get the light from the "master" unit signal to the sensor on the flash. But outdoors in bright sunlight, range and reliability are reduced, and line-of-sight requirements become more stringent. Which is why most folks favor radio triggering.

Because the YN-565EX III doesn't have any built-in radio function, if you want radio triggering, you have to look for a radio triggering system with an add-on receiver that you can attach to the foot of your flash, as well as a matching transmitter to go on your camera hotshoe. If you want full TTL/HSS communication and not just the ability to fire the flash remotely, that also means finding a set of triggers are Canon-compatible.

The Godox X1R-C receiver and any of the 2.4 GHz "X"-named Godox transmitters (X3-C, XPro II-C, or older triggers firmware updated for 2000D compatibility) would work for full TTL/HSS communication. But if you're missing the sync connector, none of the manual "single-pin" triggers (e.g., Yongnuo RF-603 II) are going to work for you. If the transmitter only has one pin on its foot, you cannot use it.

I would actually recommend switching from the YN-565EX III to a Godox TT685 II-C. It will also work on the T7's hotshoe, it has radio triggering built in. It does cost about $40 more, but an X1R receiver also costs $40. And having the convenience of your triggering being built-in, as well as a number of the nicer, newer features on the TT685 II has the YN-565EX III does not (e.g., TTL convert to Manual so you can see/lock in a TTL-set power level, a slide lock on the foot, a SCAN function to find the least-crowded radio channel, etc.) could be worth it. And you'd be in a much bigger, straightforward radio triggering system for future expansion vs. the Yongnuo world of four different radio triggering systems.