I dont know how the web-server clients or PC apps run on the bigger brand variants, but I would guess it comes with an aspect of lag and again comes down to your wireless gear, the noise of your surroundings, etc - the few examples I have seen, certainly left a lot to be desired.
I would reckon a cabled interface like fx HDMI would be preferred if its intended as a daily driver / use-case scenario
When I run Micsig STO1104C (4ch, 100mhz, 1Gbps, 28meg, 95.000 wfps) in its app to either an Android, iOS or a Windows PC.. I get this amount of lag, but that is on an old router with wifi in another room.. was like 0.3sec..
https://i.imgur.com/9K0mJxu.mp4but it's easier to just plug it in with the HDMI socket' to either my old 55" 4K OLED TV or an external monitor, as I can supply the power for the screen with the scopes 5v port, but that is more intended for mobility purpose..
I don't get touch interface control on the external screen even though it has a touch cap-digitizer, as it is over HDMI and not TypeC - but I tend to use a wireless mouse that makes it easy to manage on a big screen (like below) and away from the scope and you can swipe up and down etc for a certain menu's to pop up, like the case with the scopes touch-screen..the whole interface on this oscilloscope is intended for easy use with a mouse, or fingers, so running it on another big screen with fx a wireless mouse.. many things are optimized for ease of OS comfort.. though you also have all the bells and whistle, like a standard bench-scope with clickable rotary knobs on the scope itself.
HDMI LG OLED TV 4K 55"
HDMI to an external 5mm 15.6" 1080p antiglare touch-monitor with power supplied by the scope USB socket' but its limited how bright I can run that ext. portable screen before that poor USB2.0 5v socket don't choke"
but I recall the output is 4:3 and not natively 16:9 and obviously, these Micsig-scope are also intended for mobility, and quite far from what you're seeking if a dedicated olds style bench scope and a modern rev. of your TEK, but the support for screen or third-party iOS/Android, Windows-control is decent for a scope in its like sub 500 price range.
Controlling a scope by PC client/web server' as the main interface. - the lag & refresh rate needs to be up to the task, too not become a pain for daily use - though not sure how that stacks up in 2022 on the bigger brand models, as many reviews. don't look that much into these aspects and Im not even sure if some brands on the lower entry model. will classify it as an extra purchasable feature.