print lines between two timestamps which stamps span multiple files - sed

Question

I'm having an issue trying to accurately parse log files which time stamps may (or may not parse multiple files.
Example:
3 log files that get rotated so oldest logs are in time.log.3 and newest logs are in time.log.1
snapshot of the 3 log files
time.log.1
line 17 | 2021-03-17 21:08
line 18 | test5
line 19 | 2021-03-17 21:09
line 20 | test6
line 21 | 2021-03-18 22:10
line 22 | test7
line 23 | 2021-03-18 22:11
line 24 | test8
time.log.2
line 09 | 2021-03-16 21:04
line 10 | test9
line 11 | 2021-03-16 22:05
line 12 | test10
line 13 | 2021-03-17 19:06
line 14 | test11
line 15 | 2021-03-17 19:07
line 16 | test12
time.log.3
line 01 | 2021-03-16 19:00
line 02 | test1
line 03 | 2021-03-16 19:01
line 04 | test2
line 05 | 2021-03-16 20:02
line 06 | test3
line 07 | 2021-03-16 20:03
line 08 | test4
and so I parse them in reverse order using for loop and sed pattern match
for (( i = 3; i >= 1; --i )); do sudo cat time.log.$i | sed -nre '/2021-03-16 19:00/,/2021-03-16 19:01/p;'; done
all is good if you know exact timestamp:
line 01 | 2021-03-16 19:00
line 02 | test1
line 03 | 2021-03-16 19:01
but if I only know approx time range (like changeing it to 19:02) then because that exact pattern is not found it prints the rest of file...
for (( i = 3; i >= 1; --i )); do sudo cat time.log.$i | sed -nre '/2021-03-16 19:00/,/2021-03-16 19:02/p;'; done
yields this, but the 20:XX timestamps are outside the desire window of 19:00 thru 19:02... this is undesirable.
line 01 | 2021-03-16 19:00
line 02 | test1
line 03 | 2021-03-16 19:01
line 04 | test2
line 05 | 2021-03-16 20:02
line 06 | test3
line 07 | 2021-03-16 20:03
line 08 | test4
I need it to print only timestamps within a range, but am having trouble finding the answer... I've tried many google searches for awk, sed, perl, yet cannot land an answer... I feel I need to get past this hurdle before expecting larger time windows spanning multiple files to work...
Expounding on some of the criteria. The parse cannot happen upon the pipe (|) character, those Line number exists only to give context to the reverse order nature log file rotations and log info within the files. The parse can only happen upon the timestamps alone, and needs to contain all the "test#" info too in between the the timestamps, for not every line will have a timestamp.

Answer 1

This type of timestamp can be compared as a string. sed doesn't do comparisons, but awk does:
awk -F' [|] ' '$NF>="2021-03-16 19:00" && $NF<"2021-03-16 19:02"' time.log.{3,2,1}
Note that {3,2,1} is not a filename generating pattern (aka glob), and awk will quit if it encounters a non-existent file argument. It would be better if the files were named in such a way that log.* would work (i.e. sorted in ascending order lexicographically).
When not every line contains a timestamp, detecting if there is a timestamp might complicate things:
awk -F ' [|] ' '
$NF~/^[0-9]{4}(-[0-9]{2}){2} [0-9]{2}:[0-9]{2}$/ {x=$NF} x>=a; x>=b{exit}
' a='2021-03-16 21:00' b='2021-03-17 19:00' time.log.{3,2,1}
Or maybe the lines are grouped in pairs:
awk -F ' [|] ' '
NR%2==1 {x=$NF} x>=a; x>=b{exit}
' a='2021-03-16 21:00' b='2021-03-17 19:00' time.log.{3,2,1}
Maybe the input doesn't really contain ... | :
awk '
NR%2==1 {x=$0} x>=a; x>=b{exit}
' a='2021-03-16 21:00' b='2021-03-17 19:00' time.log.{3,2,1}