I remember looking into this during a beta phase of SQL Server (I think it was 2005). I was surprised that you even could change recovery model for master.
And, to make things more interesting, log backup isn't allowed for master.
Back in the days, SQL Server behaved like if master was in simple mode, in the sense that it would auto-truncate the log.
But below test show that this auto-truncate doesn't happen nowadays (SQL Server 2019).
Note: below will fill log for master database and ldf will autogrow. Don't run if you feel uncomfortable with that.
ALTER DATABASE MASTER SET RECOVERY FULL
BACKUP DATABASE MASTER TO DISK = 'nul'
DROP TABLE IF EXISTS t
CREATE TABLE t(c1 int identity, c2 char(80))
INSERT INTO t (c2) VALUES ('a')
DECLARE @i int = 1
WHILE @i < 100000
BEGIN
IF @i % 20000 = 0
BEGIN
SELECT counter_name, instance_name, cntr_value FROM sys.dm_os_performance_counters WHERE counter_name = 'Log File(s) Used Size (KB)' AND instance_name = DB_NAME()
CHECKPOINT
END
SET @i += 1
UPDATE t SET c2 = REPLICATE(SUBSTRING(CAST(@i AS varchar(20)), 1, 1), 70)
END
--Below result in error
--BACKUP LOG master TO DISK = 'nul'