How to make a long- lasting led light powered by button cells.

I have a very basic question. When I travel I want to pin an led housing on my book or on my shirt so that I can read my book. I used 3 button cells and a led to achieve this. But the cells run out very fast (2-3 hrs). My questions are

1. Which led I should use
2. Which button cell I should use (I cant make the device bulky)
3. Are there any rechargeable small batteries available

I cant make this too pricey!!

Do you use 3V or 1.5V buttoncells ?
A LED has a Vf that is somewhere between 2-3V. I suppose you use a current limmiting resistor. So you have a voltdrop there too (or do you use the impedance of the battery for that. In that case other Cells can damage your LED.)

The solution can be a so called joullethief. A small boost converter that squeezes the last bit of energy from the battery. I have a little flashlite build with that. It runs on a single AA battery.
https://www.circuitsonline.net/schakelingen/122/lichteffecten/witte-led-op-15-v.html I used smd for it and is the size of the battery and the pcb has to clamps to hold that battery.

As per the previous post I agree with suggestions.
I would aim for a single AA cell as they can have a good energy density. One cell (side ways or horizontal should not be too bulky).
Then "important bit" get a modern efficient switch mode circuit design chip, they are very compact and efficient to drive the LED at a constant current.
This can then work and discharge the battery to about 0.8V getting the most energy out before easily and cheaply replacing.

LED selection is personal, you need to try a few type and investigate the white colours, beam angle, over spill, (hole in the center of the beam?) etc., and may find a few smaller leds a better option. Personally I don't like the ones that give what I describe as a blue' white!

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I meant to add a few links, but look at things like ZXSC380 for the most integrated (or ZXSC300), but there are many others such as OM5448.
PA4TIM's solution can also be investigated but it is less integrated and spec'd, but may be equally suitable for you.

How long do you think ab AA battery would last in this circuit

Do you know the total wattage of the LED(s) or their Vf and current?

FWIW, the LM3909 LED Flasher/Oscillator IC was intended to maximize LED duration from a 1.5V cell (now old but maybe still available out there).
One of the app-circuits was for a booster (not a flasher) that drew only 4mA while feeding the LED with short high-current pulses @ 2kHz (constant to the eye).
But I'm sure you might have a brightness tradeoff depending on your requirement.