Do I need to do a border run to enter Thailand with a TR1 visa after my 30-day entry?

Okay you're not here on any "visa" you showed up here with no visa and you got stamped in FREE for 30 days with just an entry stamp.

You can take a 30 day extension on the entry you're on now too for 1900baht at the immigration office where you stay

𝗗𝗼 𝗜 𝗻𝗼𝘄 𝗵𝗮𝘃𝗲 𝘁𝗼 𝗱𝗼 𝗮 𝗯𝗼𝗮𝗿𝗱𝗲𝗿 𝗿𝘂𝗻 𝗮𝗻𝗱 𝗰𝗮𝗻 𝗜 𝗲𝗻𝘁𝗲𝗿 𝘁𝗵𝗲 𝗰𝗼𝘂𝗻𝘁𝗿𝘆 𝘄𝗶𝘁𝗵 𝘁𝗵𝗲 𝗧𝗥𝟭 𝘃𝗶𝘀𝗮? <- you have to exit/re-enter thailand (before that visa runs out) to use it.

Print out the PDF file as it is your visa and show it to the officer at passport control when you stamp in. They will stamp you in TR60 for 60 days