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Does the blockchain track your searches?
You mean a public block explorer website, right?
Because the Bitcoin blockchain in itself do not track your searches.
If you run your own BTC node, you can browse locally all addresses you like (using a RPC block explorer app or running your own mempool space app)
Now, a public block explorer page like blockchain.info, blockstream.info, mempool.space, oxt.me and many others could track your IP and the address you've searched.
WARNING !