SHOW PROFILE reports duplicate "Sending data" stage for INSERT...SELECT

SHOW PROFILE for an INSERT...SELECT query reports "Sending data" twice. The second entry is misleading, no data is being sent at that point.

Steps to reproduce:
CREATE TABLE profile_test (
id INT PRIMARY KEY AUTO_INCREMENT,
name VARCHAR(100),
value INT
);
INSERT INTO profile_test (name, value) VALUES
('alpha',1),('beta',2),('gamma',3),('delta',4),('epsilon',5),
('zeta',6),('eta',7),('theta',8),('iota',9),('kappa',10);
SET profiling = 1;
INSERT INTO profile_test (name, value)
SELECT name, value FROM profile_test LIMIT 5;
SHOW PROFILE;

Actual output (abbreviated):

Expected:
Stage entries reflect actual execution phases.
Actual:
A second "Sending data" entry appears after "Removing tmp table" due to a save/restore of the previous stage name inside function free_tmp_table, not because data is being sent

See also: MDEV-34900

Other query types may be affected. Under investigation.

GROUP BY:
SELECT name, COUNT( * ) FROM profile_test GROUP BY name;

Actual output (abbreviated):

is affected by the same save/restore pattern inside free_tmp_table