Add-on store in homeassistant

Hello !

I hope this is the correct category for my question. Please forgive me if I am wrong!

My question: What can I do to get the add-on store integrated into my fresh installation of HA? And - if there is no way at all to get the store integrated - which installation method (Raspi/SD/SSD cards are no go for me) can be used in order to access the store?

All the solutions I found so far point towards hass.io which is seemingly no option. anymore. RTFM did not bring up any idea so far either. I am kind of stuck.

So far I used the store to get add-ons like ESPHome and HACS to mention the most important add-ons for my setup.
Here is my setup:

Short story:
The problem I am facing is that the add-on shop does not show up in the browser. I learned that the add-ons can be manually installed, but every search result points to using the add-on only. A bit frustrating…

The long story:
I had a running hass.io / docker setup which I created using My idea was to create a new home for my HA setup from scatch as I wanted to switch to the latest LTS of Ubuntu. As hass.io is deprecated I did some research and selected the alternative installation in a venv.
I chose the installation method mentioned above as I did not have a Raspberry Pie (using HassOS) nor did I want to use a virtual machine not docker. Hass.io and docker would have been my favourite choice, but as this option is deprecated… ;-(

Thank you in advance for any hint!