Populating a field in one table with text value from another table

So to preface this, I'm not really a "database guy" per se, I'm much more of a spreadsheet guy, and it's been a while since I've built a db. I'm mostly relying on my scripting experience in other scenarios (batch and BASH basically, and I can stumble my way through reading a JS query), but so far this has been failing me. 

Excuses out of the way, I'm working on a database for a trading card collection. It has two tables, which we'll refer to as T1 and T2. T1 is the "main" table that lists all of the cards, and T2 is a ban list. What I'm trying to do is set up a field in T1 that will compare T1.Name to T2.Name and when a match is found, show the value from T2.LVLban, otherwise it should show as "Unlimited". I had this set up in Excel using the XLOOKUP function and it did what I wanted it to, but the list is over 10k records, so Excel wasn't really able to cope with the load.

So far I have tried various permutations of the following formulas, with the goal of populating the field T1.LVLban: 

if T1.Name = T2.Name then T2.LVLban else "Unlimited"

and 

if T1.Name = T2.Name and T2.LVLban = "Forbidden" then "Forbidden"

else if T1.Name = T2.Name and T2.LVLban = "Limited" then "Limited"

else if T1.Name = T2.Name and T2.LVLban = "Semi-Limited" then "Semi-Limited"

else "Unlimited"

I've tried these in both a formula field and in a table reference field with no luck so far. I feel like the logic itself should work (or that it at least makes sense), I'm just not confident in where it needs to be entered. I've been searching through the docs and so far everything I've come across hasn't actually gotten me where I'm trying to go, so any guidance or suggestions you could provide would be greatly appreciated.