The Pocket 386 gets its name from its 386 SX compatible processor, and the system should be able to run MS-DOS and Windows 95, but isn’t going to good for anything much newer than that.

The Pocket 386's screen is higher-quality, though, ... DOS/Windows 3.1x. The aging 386 had already been replaced by the 486 by the time Windows 3.x hit in the early '90s, ...

And then there’s the Hand 386. It’s a handheld computer ... and a 40 MHz Intel 386sx-compatible processor that supports MS-DOS, Windows 3 ... The display is a 740 x 480 pixel screen ...

Per the listing, the handheld is suitable for Windows 3.1 – Windows 95 / MS-DOS 6.22 – 7.1. The specs also reference a USB connector, an 8-bit ISA port, a 3.5 mm audio out jack, a VGA output ...

Alternatively, there are other DOS browsers, I believe. Breadbox Ensemble (PC GEOS derivative) has had a browser, I think. But it may need a 386+, not sure. And it’s even more behind the times ...