MySQL 8.0

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create table morning as
    select 1 as id, 'bla ' as text, '2020-08-07 10:30:00' as timestamp union all
    select 2 as id, 'blub' as text, '2020-08-06 11:30:00' as timestamp union all
    select 3 as id, 'abc ' as text, '2020-08-05 09:20:00' as timestamp union all
    select 4 as id, 'def ' as text, '2020-08-04 06:13:00' as timestamp union all
    select 5 as id, 'ghi ' as text, '2020-08-02 07:05:00' as timestamp 


Records: 5  Duplicates: 0  Warnings: 0


create table evening as
    select 1 as id, 'abc' as text, '2020-08-07 19:30:00' as timestamp union all
    select 2 as id, 'def' as text, '2020-08-06 20:45:00' as timestamp union all
    select 3 as id, 'ghi' as text, '2020-08-05 21:30:00' as timestamp union all
    select 4 as id, 'jkl' as text, '2020-08-03 20:13:00' as timestamp union all
    select 5 as id, 'mno' as text, '2020-08-01 17:33:00' as timestamp union all
    select 6 as id, 'pqr' as text, '2020-07-29 19:19:19' as timestamp 

Records: 6  Duplicates: 0  Warnings: 0


with me as (
      select dte
      from ((select date(timestamp) as dte, 1 as morning, 0 as evening
             from morning
            ) union all
            (select date(timestamp) as dte, 0 as morning, 1 as evening
             from evening
            )
           ) me
      group by dte
      having sum(morning) > 0 and sum(evening) > 0
     )
select min(dte), max(dte), count(*)
from (select dte, row_number() over (order by dte) as seqnum
      from me
     ) me
group by dte - interval seqnum day
order by count(*) desc
limit 1;


min(dte)
max(dte)
count(*)


2020-08-05
2020-08-07
3


select min(dte), max(dte), count(*)
from (select dte, (@rn := @rn + 1) as seqnum
      from (select dte
            from ((select date(timestamp) as dte, 1 as morning, 0 as evening
                   from morning
                  ) union all
                  (select date(timestamp) as dte, 0 as morning, 1 as evening
                   from evening
                  )
                 ) me
            group by dte
            having sum(morning) > 0 and sum(evening) > 0
            order by dte
           ) d cross join
           (select @rn := 0) params
     ) me
group by dte - interval seqnum day
order by count(*) desc
limit 1;


min(dte)
max(dte)
count(*)


2020-08-05
2020-08-07
3