MySQL 8.0

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CREATE TABLE A (id int, status  varchar(10), when_modified  datetime)
INSERT INTO A VALUES (1,'finished',now())
CREATE TABLE B (id int, block int)
INSERT INTO B VALUES(1,0)
Update B vv JOIN A  v on vv.id = v.id SET vv.block = 1, v.when_modified = NOW()  WHERE v.status = 'finished' 

Rows matched: 2  Changed: 1  Warnings: 0

SELECT * FROM A

id
status
when_modified

1
finished
2023-05-15 20:31:15

SELECT * FROM B 

id
block

1
1