Is the door metal?

Or there's a blind enclosed in glass that fits over your existing window.

https://www.lowes.com/pd/ODL-Add-on-blind-0-59-in-Slat-Width-22-in-x-36-in-Cordless-White-Aluminum-Light-Filtering-Mini-Blinds/5014977491

Look for a No Drill Blind.

Drilling into a door while void any warranty and could also cause other problems, not to mention break the glass.

https://www.amazon.com/BERISSA-Darkening-Office-Easy-Install-SY-Brown-Custom/dp/B0DDXX35X7/ref=sxin_17_pa_sp_search_thematic_sspa?content-id=amzn1.sym.9f01143a-7bae-4523-a6b2-a548b467f90e%3Aamzn1.sym.9f01143a-7bae-4523-a6b2-a548b467f90e&cv_ct_cx=no+drill+blinds&keywords=no+drill+blinds&pd_rd_i=B0DDXX35X7&pd_rd_r=5010a486-c8cb-4eb8-ba59-21c885ca3c39&pd_rd_w=TQJWF&pd_rd_wg=ygq8D&pf_rd_p=9f01143a-7bae-4523-a6b2-a548b467f90e&pf_rd_r=5Y00V8K389YHKT1A1KN0&qid=1766005198&sbo=RZvfv%2F%2FHxDF%2BO5021pAnSA%3D%3D&sr=1-4-28dec9df-ff35-40b5-8e68-2d1c97dfc4dc-spons&aref=PEHIC6bBi9&sp_csd=d2lkZ2V0TmFtZT1zcF9zZWFyY2hfdGhlbWF0aWM&psc=1

Blinds are essentially rather ugly, and "No Drill" blinds are INSIDE mount only. You have an outside mount.

You are NOT going to hit glass. Get a CORDLESS cellular shade, translucent, Yes, it will still afford privacy, but will "disappear" when you don't need it down. Readily available online, simple white white:

Install:

Installation Steps

1. Drill Pilot Holes: For steel or fiberglass doors, use a 1/16" metal drill bit to create pilot holes. If using a steel door, self-tapping screws can be used to bypass pre-drilling.
2. Attach Brackets: Screw the mounting brackets into your marks. Ensure they are level before tightening completely.
3. Snap-In Headrail: Hook the front of the shade's headrail onto the brackets and rotate it upward until it clicks into place.
4. Install Hold-Down Brackets (Crucial): To prevent the shade from swinging away when the door opens, install hold-down brackets at the bottom of the door. These small L-shaped brackets catch pins on the bottom rail of the shade.
5. Done...............: ) I would skip the hold down brackets: )

You should take Jan Moyer's advice. In my experience unless the blind is built inside the doors glass cavity they often will swing too much when the door is opened and closed.

The glass doesn't extend much beyond the visible pane, so you shouldn't hit glass when drilling. I installed cordless shades as described by Jan above on a French door without any problems.

Looks like the neighbour’s window is directly across and wonder if a film is a better solution for both day and night privacy. Easy/inexpensive with lots of design options (some will allow more light to filter through).

^^

They tend not to stay adhered.......which is rather a big BUMMER: )

I’ve used the film on the inside of garage windows and it stayed on very well. My previous home’s window washer could wash and squeegee with no problem. Follow directions carefully when applying.

You can get some really cool inserts to replace that glass I got one from Homedepot for a regular window from a big box store . Or a flim is really the only answers I would not want to drill into an exterior steel door

I have done the window film on a door
Exactly like yours. Easy peasy, looks great, nothing gets dusty, adheres perfectly. Make sure you clean the window pane properly, let dry, the adhere the window film.