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Why is coffee provided for free during big chess events like the Olympiad despite the fact that it contains caffeine, which is a banned substance according to the World Anti Doping Agency (WADA)?

It is not prohibited would be the main answer.

Caffeine was removed from the list, and moved to the WADA "watch list", so it is not currently banned. "Bupropion, caffeine, nicotine, phenylephrine, phenylpropanolamine, pipradrol, and synephrine: These substances are included in the 2019 Monitoring Program, and are not considered Prohibited Substances." (quote taken from both the 2019 and 2020 WADA prohibited list PDF document).

"The legal limit under previous restrictions was 12 microgram/ml in urine, which is roughly equivalent to drinking 8 servings of espressos over the course of a few hours." (quote taken from nationalcoffee.blog)

According to FIDE's Anti-Doping Policy:

The 2018 WADA Prohibited List and Monitoring Program can be found at:
http://list.wada-ama.org/
The most relevant banned substances for chess are:

• Amphetamines – e.g. Adderall, Ritalin

• Ephedrine and Methylephedrine – Prohibited by WADA when its
concentration in urine is greater than 10 micrograms per milliliter

• Pseudoephedrine is prohibited when its concentration in urine is greater than
150 micrograms per milliliter

• Modafinil

Substances not present on the Prohibited List but represented in the Monitoring
Program:

• Caffeine – Included in WADA Monitoring Program and relevant for incompetition testing only. Any urine test reading of less than 12 micrograms per milliliter poses no problem.

• Codeine – A common ingredient in, for example, preparations used to treat coughs and stomach upsets. Any dosage is highly unlikely to be significant when taken in normal therapeutic quantities.

Note that caffeine is not currently banned. It was banned during the period 1984 - 2004 but was lifted. I'm guessing that sponsorship via advertising from Coca Cola may have been an important factor.

Because nobody seriously considers it an advantage in chess. The WADA applies to sport, where caffeine can improve performance because it's a stimulant, thus improving physical performance. In chess, however, physical performance is meaningless, and no one has ever performed a test that proves caffeine leads to better chess (as opposed to, say, faster times in a race). Indeed, since one of its side-effects is an increase in impulsiveness, it could very well prove a detriment to playing better chess.

I can see where it might yield a minor advantage in blitz, where fractions of a second in punching the clock would matter. But in normal tournaments, I'd wait until someone actually does some testing before worrying about any substance.