[Moderator's note: The James Webb Space Telescope is more like a
traditional telescope in space, the successor to HST in some sense, but
with more emphasis on the infrared.

JWST wavelength range is roughly 0.6 to 27 microns

The CMB is observed at lower frequencies

much longer wavelengths than JWST.

As far as I know there is no CMB satellite in the works,

same here

but some ground-based stuff such as the Simons Observatory. -P.H.]

I think there's quite a lot of ground-based work. Most familiar to
me is South Pole Telescope:
https://pole.uchicago.edu/

There's also BLAST, a balloon telescope:
https://sites.northwestern.edu/blast/

They've done CMB work in the past, but the upcoming flight seems to
be Galactic objects.

All ground-based and balloon telescopes study relatively high
multipoles, i.e., relatively small angular scales. I think it's only
the lower multipoles that carry information on H, but I may be wrong.

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