I use the Templater plugin to create my daily note, with something like below, so the today gets translated to hardcoded value. This way, going back to a previous Daily Note, the value is hardcoded and therefore preserved at that point in time.
modification date: <%+ tp.file.last_modified_date("dddd Do MMMM YYYY HH:mm:ss") %>
<%*
let yesterday = tp.date.now("YYYY-MM-DD", -1, tp.file.title, "YYYY-MM-DD")
let today = tp.date.now("YYYY-MM-DD", 0, tp.file.title, "YYYY-MM-DD")
let tomorrow = tp.date.now("YYYY-MM-DD", 1, tp.file.title, "YYYY-MM-DD")
%>
[[<% tp.date.yesterday("YYYY-MM-DD") %>]] <== <button class="date_button_today">Today</button> ==> [[<% tp.date.tomorrow("YYYY-MM-DD") %>]]
## Tasks
### Over Due
```tasks
not done
due before <% today %>
```
### Today
#### Due Today
```tasks
not done
due on <% today %>
```