As you mentioned, you can use Windows File Explorer/File Explorer Search to select the photos you want to edit the EXIF data for and then use Properties > Details from the right-click menu and put a date into the 'Date Taken' field.
However as you also mentioned Microsoft don't allow you to adjust the time. With old scanned photos this is particularly problematic because quite often the exact date isn't known and therefore an approximate year is used as 'Date Taken' for lots of photos (I.E. Date Taken = 1970.06.01). But without being able to adjust the time, it will use it's own timestamps and therefore when viewing the photos in something like the Windows Photos app that uses 'Date Taken', the order it will display the photos in will be all over the place.
When I looked for Batch EXIF editing software a while ago, I didn't come across anything that suited my needs, so I ended up forgoing a user interface and using a command-line tool called ExifTool instead. ExifTool is capable, but it's not for the faint hearted, the website/documentation even less so... However, if you don't mind using this type of tool from Command Prompt, then maybe the below will help.
1) Download "Windows Executable: exiftool-10.30.zip" from this link:
ExifTool by Phil Harvey
2) Extract "exiftool(-k).exe" from the zip file, save it somewhere and rename it to "exiftool.exe" for command-line use.
3) Put the photos that are all going to be of the same 'Date Taken' in the same folder. I.E.
1971.03.15 Peter Pan's Wedding
1971.06.20 Holiday in Timbuktu
4) Whilst in that folder, hold the Shift Key and Right-Click mouse, then select 'Open Command Window Here' to open the command prompt at that folder location
5) Use the following code:
IMPORTANT: Make a copy of the folder and do a dummy run first. That way you will have a copy of the original folder you can always go back to if you don't like the results.
"C:\Users\USERNAME\Software\ExifTool\ExifTool 10.28\exiftool" -overwrite_original -datetimeoriginal="1971:01:30 00:01:00" .
"C:\Users\USERNAME\Software\ExifTool\ExifTool 10.28\exiftool" -overwrite_original -fileOrder FileName "-datetimeoriginal+<00:00$filesequence" .
Change the above paths to exiftool (C:\Users\USERNAME\Software\ExifTool\ExifTool 10.28\exiftool) to match the path where you saved the exiftool executable.
Change "datetimeoriginal" to the date the photos were taken
What the above code does is goes through the photos in the folder in File Name order (Hence the -fileOrder FileName) and changes the date taken to 1971.01.30 at 00:01, then goes to the next image in the folder and changes the date taken to 1971.01.30 at 00:02, then the next and changes the date taken to 1971.01.30 at 00:03... and so on. Although the times aren't obviously accurate, the minute increments will put the photos in a sequential order.
It's done in this way for two reasons, firstly for me all my digital images already have the correct 'Date Taken' field, so this is targeted specifically towards scanned images. Secondly, I've always found file timestamps such as Date Created, Date Modified and Date Accessed to be largely unreliable to base batch processing off, so I would use my own dates even if it meant that it's more time consuming. That said, you may be able to find a way to use filemodifydate to populate the Date Taken field, but like I said it's not something I've wanted to use. ExifTool has also has it's own forum if you can't find what you're looking for on Google Search.
6) The 'Date Taken' field will now show the date taken, with time in minute increments so they display in the correct order in applications that use 'Date Taken'.
Something to be aware of, ExifTool is only 32-bit, therefore if your photos need dating before 1 January 1970 (or after 19 January 2038) it's a bit more complicated as you will need to install ActivePerl and then use the Perl version of ExifTool. As the Perl version is 64-bit it can handle dates before 1 January 1970. Installing the 'Full Perl Distribution' instructions can be found HERE.