I can see why the brackets might seem too tight but I'd bet the bulb does "just pop out" of them. I'd put my thumbs on the piece between the bracket and the middle (to make it stay put and not pull down). put my fingers on the outside of the light bulb, and firmly pull with my fingers. Then do the same to the other side.

I think the safest way to try is to push up on the ends of the arms, rather than pulling the bulb down.

They just pop out of the holders and then you unplug the electrical connection.

Whatever you do, wear eye protection in case the bulb breaks!

My Grandmother was short and had a lot of these lights, so being taller I was tasked with replacing them a lot. When I got her house I changed them out to different lights, so I have not seen them in awhile. I am sure you can get replacements though.

2/26/23 UPDATE: Thank you! for all of the information and advice. I had to wait until the weekend to tackle this in daylight. It is a dark walk-in closet. I also had more time to think about it. I still used a flashlight and thoroughly examined the fixture and bulb. I then attempted to bring the bulb to the furthest stress point where any further might break the bulb. Once there I looked carefully with the flashlight and realized I was right at the widest portion of the circumference and knew I could pop out the bulb safely without risk of damaging anything. Now that the bulb has been removed I can see the part number. I am not sure whether the replacement bulb I had purchased in advance is compatible so I am going to bring the old bulb back to the hardware store and have someone there confirm or recommend a different bulb. Thank you again!