is there better format than PNG to store R16uint depth data as ASTC has precision artifact on Android?

There are no lossless hardware texture compression formats. There are pros and cons to the various formats of ASTC, ETC2, PVRTC, and S3TC / DXTn, but none offer lossless encoding. You can use plain data buffers, but they are not hardware texture compression formats.

As an image format, png is kind of mediocre. It's lossless (which, all else being equal, is good), but its compression ratio is usually worse than lossless webp or even uncompressed raw data put through a strong general purpose compression algorithm like lzma. There is no one best format – it depends on your requirements and your data – but it wouldn't be my first choice.

As a container for non-color data, png is still kind of mediocre, but webp isn't really an option. Raw data + general purpose compression algorithm is an option if file size is important to you, and raw data without compression is an option if file size doesn't matter at all to you.