Don't thank me too soon.
I am unable to reproduce your issue in my network.
My hope was that your config would look similar to doncarajo's, which binds to IPv4 and IPv6 localhost alike, in an attempt to use their observation of Turning off "Enable IPv6 support (SLAAC + RA)" solving their issue to support a theory that eliminating IPv6 from
unbound's config could also avoid the issue.
However, your configuration is already limited to IPv4's
127.0.0.1 interface, so that theory of mine isn't working.
I don't think this is a Pi-hole issue:
unbound stops and restarts gracefully, so somethng seems to send a regular
kill -HUP to
unbound, presumably on change of an IPv6 RA - probably an IPv6 prefix change. Both such a change of a prefix as well as
unbound reloading to adopt to such a change seem reasonable at first glance (but then I vaguely recall doncarajo mentioning that he's got a fixed IPv6 prefix).
It would seem logical to attempt to influence the frequency of RAs, which may be configurable via your router, but may also depend on a client's configuration or even on your ISP, in which case it would be out of your control.
This is just me speculating, however.
This will likely be quite hard to analyse, especially if we fail to reproduce it.
You could start by trying to find out which process is signalling
unbound to stop and restart.
Depending on how that turns out, we may quickly reach the point where we cannot provide further meaningful assistance from a Pi-hole perspective.
It may be advantageous to consider to consult other support channels as well, specifically
unbound's mailing list, since that is the software that exihibits unwanted behaviour.