There are no Shimano brifters that are 2x11 compatible, but Microshift manufactures some. I use a Microshift SB-110 (1x11) and a bar-end shifter for a drop-bar 3x11 setup with an XT rear derailleur (RD-M8000) and XTR front derailleur (FD-M9000) with no issues.
Here is Microshift's product page for the SB-110: https://www.microshift.com/en/product/sb-m110/
As already noted in other answers, there is no compatible unit. The pull ratio is different.
However, given the typical prices of brifters and derailleurs, I think it would be better to buy a new 11-speed derailleur that is compatible with your new brifters - such as the Shimano GRX.
It will be better than some extra units for pull ratio conversion.
Unfortunately 11 speed MTB and 11 speed road have different pull ratios.
You could use this adapter/converter: https://www.wolftoothcomponents.com/products/tanpan
It should allow you to keep using your existing rear derailleur and cassette.
Assuming your shifters are SL-M5100
Then the product matrix at https://productinfo.shimano.com/#/com?cid=C-432&acid=C-435 says no.
Sadly the "gravel bike" specific groupsets are based on ...