Will this trigger significantly degrade performance?
The best way to evaluate performance is by measuring it- you are the only person that can evaluate that on the real application, or, much better, on a staging environment with a copy of the traffic or an emulation of such.

Hardware, other code running, throughput, how slow are those new queries, amount of data you have, etc. will tell you what you want to know- to the point that the same code can make it or break it under different circumstances.

Having said that, if you just want a high level opinion of the idea will work, without knowing much about your system- I would personally would do this kind of analysis asynchronously based on external logs (or your login_att table), as normally you don't want to punish your normal users if the occurrences are not frequent enough. Also triggers are not my favorite way to handle application logic. However, if you cannot modify the source code, it doesn't add much to the total latency, and you test it and it seem acceptable, go on- but please test it doesn't break your application when there are thousands of parallel attempts per second due to the extra writes.