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I’m not a fan of relying on the no-name budget lights (typically 3 x AAA) for a true emergency due to how flaky they can be. I can think of 5 of these lights of three different designs still floating around my house from the days of being a recent graduate when I wanted something with better runtime than my old Maglite Mini, but was too cheap to even buy another Maglite.

All of them have low quality switches that seem to gradually get worse over time (corrosion?) and often require a hard shake to get a good connection. When they do work, the output is wildly inconsistent due to lack of regulation. The tints are terrible (which can be relevant to first aid). Often they are bulky for what they offer.

The Fenix E01, Sofirn C01, and Gerber Infinity Ultra are all well made, highly efficient, long runtime lights I’d recommend. The C01 has the bonus of high CRI, even if the low output makes that mainly relevant within a couple feet.

For something with more output, the Sofirn SF10 is one I’d probably consider. The SF14, Lumintop Tool AA, and Convoy T2 are all similar, with a bit more output.

If you ever felt like having a backup to your emergency lights, you can buy multi-packs of the little coin cell squeeze lights for around $1 each. Similarly, these are really low cost/weight/size light you could keep on hand and just dispose of when it dies:
https://www.lowes.com/pd/Panther-Vision-Button-Lamp-13-Lumen-LED-Miniature-Flashlight-Battery-Included/1000494525