I have a Samsung smart tv and I had difficulty accessing server so I signed out. Now I can’t sign back in as the screen that shows the code shows no numbers
Your TV is too old. It cannot communicate with plex anymore.
It has been running a very old app, that was made by a community developer. It is abandoned for several years by now.
Will getting a streaming stick solve the problem?
As long as that streaming stick is able to run an offical Plex client, yes.