I create notes with date property and assign date, it shows the link icon, send that to the daily note, but there is not shown the backlink to the note with the date propery.
Backlink view for the day note show notes with the date property set to that date.
Can use another property link to the daily note, but is redundant.
+1 from me. Would help to avoid having to create a text field with [[YYYY-MM-DD]] just to have linked dates. Reduces what could result in duplication of effort
In addition, it would be good to have a built-in conversion so that in the “Properties” pane, one could convert a text-based date property to a date-type property in all notes
E.g., currently I have
date: [[YYYY-MM-DD]] where date is a text property and I have added the date manually as a link.
When/if the ability to add dates as links to date-type properties is developed, it would be nice if changing a text-field, as above, to a date-field automatically reformatted the value in the correct way, while maintaining the link.
edit: sorry if I described this badly.
I’d like to see this too. It’s how I expected YAML frontmatter in Obsidian to work in the first place and it’s been frustrating to work around it (for 2+ years). I’ve just avoided using frontmatter due to all the issues with Obsidian not interpreting tags and other text within it (if only that energy could be used when deciding what constitutes a backlink, eg URLs being seen as possible matches)
If YAML is being promoted as a supported feature then these links should work as date references within the app.
+1 indeed. I have a created date, and modified date(s), in format [[YYYYMMDD]], in every note, and so I can open a daily note at any time and see what I was doing on that day via the backlinks function. As @ryadaj says, this means the date fields in the properties section need to be either removed or duplicated. Ability to link date fields, as we can text and list fields, is the solution
+1 from me. It would allow us to see what we were doing on that day via the backlinks.
+1 from me.
I’m still trying to decide whether I want date properties that are of type date so that I can perform date math, or whether I want them to accept links to my daily notes so that I have the temporal references.
I’m unfortunately in a spot where I’m doing both right now because I can’t decide, and I’m ending up with a proliferation of “Date added,” “Date created,” “Date originated” and so forth. I’m running out of synonyms for “create”. 
+1, would be great to have the date property act as a full link, and thus enable all the network features of links
+1, not being able to see notes with the metadata date show up in the Linked mentions section for that daily note is pretty annoying since now I need to maintain two date fields in the metadata. Or add a DataView into every single daily note with a query for the file’s date.
Having backlinks for property dates would be really helpful! Hopefully the team can considering adding it.
+1, I was surprised to see this was not default behaviour. Plus linking the date in the date field also does not work, so duplicating with date-link as suggested by @n-patel is necessary (but annoying!).
+1, this is exactly how I would hope this to behave.