PNG, 96 bytes
After reading this article and becoming more familiar than I would ever want to with these docs, I've created a PNG solution. It's definitely not optimal. I haven't quite figured out the compression entirely yet. Anyway, here it is:
00000000: 8950 4e47 0d0a 1a0a 0000 000d 4948 4452 .PNG........IHDR
00000010: 0000 004e 0000 0034 0103 0000 001e dd9c ...N...4........
00000020: f900 0000 0650 4c54 4500 57b7 ffd7 00df .....PLTE.W.....
00000030: 10bb 0200 0000 1549 4441 5478 da63 6018 .......IDATx.c`.
00000040: 0578 c07f 18f8 33ca c460 0200 8b3d 02be .x....3..`...=..
00000050: 44c1 a979 0000 0000 4945 4e44 ae42 6082 D..y....IEND.B`.

I'd recommend downloading it and checking it out on this useful page which shows the structure: https://evanhahn.gitlab.io/png-explorer/
It's also linked from the first article.
In summary, it contains these chunks. You can see them in the ASCII decoding of the bytes.
PNG A signature chunk saying it's a PNG file
IHDR A header chunk with the width, height and colour type, and some other stuff. This image is "index color", meaning it has a palette of colours which it picks from for each pixel.
PLTE A palette chunk containing the two colours. You can see these in the bytes near the end of the third line as 4500 57b7 ffd7 00df, which is the two hex colours next to each other.
IDAT The image data chunk itself (this is a scanline for each row, which is either zeros or ones depending if it's blue or yellow). It is compressed losslessly.
IEND An "end" chunk
Some optimisations to be had:
- The end chunk seems to be able to be removed, although this is in violation of the spec. Saves 12 bytes.
- The article also links to this website which allows you to generate a single colour image. It somehow has better compression and I couldn't get my zlib to do it. It saves about 4 bytes.
So it's probably possible to get down to 80 bytes quite easily. Beyond that:
- You could probably use the background colour and omit half the scanlines. Again, this would probably be in violation of the spec. It also may actually use more bytes.
- You may be able to use pixel aspect ratio to use less pixels
Here's the awful code I threw together to create it: https://pastebin.com/tjdrQ4md
#fbd02aand the blue is#1a54b2, as opposed to the#ffd700and#0057b7specified in the text. \$\endgroup\$