Bitcoin’s taproot upgrade was initiated this month, and the network is able to send and receive Taproot transactions, or at least in theory. Echanges and wallets still need to be upgraded, and @murchandamus is keeping track of this on Bitcoin Wiki.
So far there is only a small amount of Bitcoin stored in a P2TR(Taproot) Output, less than 2.5 Bitcoin. This seems to be growing as more and more exchanges and wallets start showing support through upgrades. The open source community is working on solutions and it is very interesting to see this turn out in real time.
When looking at SegWit, it was a slow and gradual climb that curved upward over a month and a half period, then tapered off and went flat. It took segwit almost a year to reach more than 30% adoption and part of that is only because BitcoinCore implemented it. Bitcoin just recently hit 85% segwit adoption which took more than 4 years.
Currently if you send a Taproot transaction to a non-taproot address, you may not get your Bitcoin back. Luckily, most wallet providers and exchanges will not let you send it to an unsupported address. It's unknown how long it will take for wallets to upgrade, but it's safe to say it will be a few years.
Taproot, simply explained, allows for schnorr signatures where multisig transactions are indistinguishable from a single signature, creating more privacy for the network. In future improvements, this allows for Schnorr Signature Aggregation that essentially makes it more efficient to batch transactions together in a coinjoin for more privacy to the network.
It may take years for the improvements of taproot to be actionable and in the meantime, developers will be working on integrating it into their wallets, along with all its benefits. Taproot was a soft work so there wasn't as much controversy over it, meaning everything is backwards compatible. There is still much work to be done, but the network has upgraded and the community is making developments as we speak that will impact Bitcoin for decades to come.