How to sort data on the closest distance basis in QGIS?

I’m preparing a map in QGIS 3.16.5 with the set of points and polygons in two layers. Unfortunately during a field work data were collected a bit randomly and objects of subsequent names are scattered on the map (by object I mean both: points & polygons). For instance, I have an object named 100 very close to object 1, while object 2 is located in a large distance. I want to rename objects to get some logical order of the names. I was going to export data to .csv, then change names in spreadsheet and import it again to a new layer.

Before that I need to sort data somehow using location and distance between objects as a rule. I would like to have object no. 1 in the first row, then, in the second row, the object that is closest to 1, in the third row object that is closest to this from the second row, in the fourth row object that is closest to this from the third row, and so on. In the end I would like to have numbers assigned respectively to each object.

Can it be done?