Find all stats that were sampled
You can see how many rows were sampled (among other things) by using the sys.dm_db_stats_properties DMF:

SELECT object_name(s.object_id), s.name, 
       sp.last_updated, sp.rows, sp.rows_sampled, 
       sp.steps, sp.unfiltered_rows, sp.modification_counter
FROM sys.stats s
CROSS APPLY sys.dm_db_stats_properties (s.object_id, s.stats_id) sp
WHERE s.object_id = object_id('TableName')
AND s.name = 'IndexName';


You can add some math to do the comparison for rows_sampled vs rows. Given that there will be data movement in the table after you update stats, I wouldn't expect this to be 100%, but you can assume that if a full scan was done, you'll see at least 80% of the current table size:

SELECT object_name(s.object_id), s.name, 
       sp.last_updated, sp.rows, sp.rows_sampled, 
       --
       sample_percent = (100*sp.rows_sampled/sp.rows),
       --
       sp.steps, sp.unfiltered_rows, sp.modification_counter
FROM sys.stats s
CROSS APPLY sys.dm_db_stats_properties (s.object_id, s.stats_id) sp
WHERE s.object_id = object_id('TableName')
AND s.name = 'IndexName';


Now, you just have to use some tool to run it against your thousands of databases. I suspect that if you're managing thousands of databases, you already have an established way to do this. As a PSA, I'll mention that sp_MSforeachdb sometimes misses databases, so consider avoiding that stored procedure.