When autovaccum will analyze?
The formula is correct.
The number of live rows is taken from the reltuples column in pg_class, and the result of the formula is compared to n_mod_since_analyze from pg_stat_all_tables.
Note that autovacuum_analyze_scale_factor and autovacuum_analyze_threshold can be overridden by storage parameters on th table.
If all available autovacuum workers are running (autovacuum_max_workers), you may have to wait.
Analyze only takes an ACCESS SHARE lock on the table (it only reads), so it can run concurrently with almost anything. Like a SELECT statement, it will see the rows that are visible to it.
If you need a table to be analyzed between an INSERT and an UPDATE, don't wait for autoanalyze to run. Explicitly start ANALYZE on the table.