Homey (Early 2016) keeps showing the orange loading animation and is offline during that time

Did you replace the power unit as well (5V and 2A or more)?

When you have a recent backup, a factory reset and then a restore of the backup should bring Homey back in the state of what it was when the backup was made.
You can even restore a Homey to a brand new Homey that way. Flows, devices, everything should work.
Only community store apps, and apps installed by CLI have to be installed by yourself.

For now, I’d like to advice to start Homey in recovery and perform a ‘full software download’.
That can solve vague issues like your Homey show.