Looks like your UV islands are pretty loosely packed . Modern UV packers could do much better usually . It could give you more pixels per certain detail. Then you can bend /deform other islands slightly for tighter pack , just slightly. Then you could upscale the island having this sign a bit. It may sound like blasphemy and against everything you read about "steady texel density " but sometimes bending the rules a bit helps. Nobody notice different texel size on just white thing . You also could make sure the island having this sign is not deformed or rotated . Rotate others instead . It's a case of no perfect solution , you just sacrifice something else.
Also be sure you work in doubled resolution in Painter and downscale at export . Painter is notorious for being a bit blurry because all those projections it uses operate not within per pixel precision like Photoshop and such.
I also sometimes use Affinity Photo with Lamczos3 non-separable pixel interpolation for that down-scaling . Maybe it's just self persuading and an illusion but I think it gives a tiny bit better look. Worth a try if you have it but it's like 5% , other 95 is unwrap for more pixels and straighter orientation .
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