This depends on how much effort you would like to spend.
Solution 1 (recommended):
I am just feeding my data to OpenSky from a Raspberry Pi and consume this on my other computers via the OpenSky Python-API.
The dump1090 or dump1090-fa usually provides output data on port 30005 in the Beast format. It may take some time to find out how to consume it.
Open the web interface of the dump1090 in your web browser and use the developer tools of the browser to analyse data access. There might be calls like "http://your-raspi:8080/data/aircraft.json?_=1639944660718" which provide JSON output.
This could easily be interpreted by python using "requests":
response = requests.get("http://...").json()