Hi Zaxxer,
welcome to the Apple (user-to-user) Community.
Re: "Cannot connect to HomePod 1: I have been having issues with my HomePod 1
with it losing the connection to the internet"
See if anything in Apple support's articles can help:
Eg: If Siri on your HomePod says it can't connect to the internet
Resolve Wi-Fi and Bluetooth issues caused by wireless interference – Apple Support
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Re: "I have updated my phone and iPad to the latest iOS"
About Software Updates for HomePod - Apple Support
How to: Update HomePod - Apple Support
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Re: "I did a full reset of it and since then I cannot connect to it at all."
You might want to try
Pressing the top of HomePod to reset it instead,
and following the instructions that follow in that section:
Reset HomePod
What to do: If HomePod or HomePod mini isn't responding - Apple Support
Maybe check through: Set up HomePod – Apple Support for tips
and
What to do: If you can't set up HomePod or HomePod mini - Apple Support
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Resource:
HomePod user guide:
https://help.apple.com/homepod/
More support:
HomePod Support Website:
HomePod - Official Apple Support
And
If nothing above has helped:
There is a "Support" link to Apple on right of top menu on this discussion page.
or
See a list of Apple support and service phone numbers around the world:
Contact Apple for support and service - Apple Support
All the best :-)