MySQL 8.0

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create table sample (id int, ts timestamp);
insert into sample 
        values row(1, '2023-01-01'),
               row(2, '2023-01-02'),
               row(3, '2023-01-03'),
               row(4, '2023-01-04');

Records: 4  Duplicates: 0  Warnings: 0

select  from_unixtime(avg(unix_timestamp(ts)) over
            (rows between 1 preceding and current row))
from    sample

from_unixtime(avg(unix_timestamp(ts)) over
            (rows between 1 preceding and current row))

2023-01-01 00:00:00.0000

2023-01-01 12:00:00.0000

2023-01-02 12:00:00.0000

2023-01-03 12:00:00.0000

select  from_unixtime(avgts)
from    (
        select  avg(unix_timestamp(ts)) over
            (rows between 1 preceding and current row) as avgts
        from    sample
        ) s

from_unixtime(avgts)

2023-01-01 00:00:00.0000

2023-01-01 12:00:00.0000

2023-01-02 12:00:00.0000

2023-01-03 12:00:00.0000