No single file format currently fits your requirements. Your current solution is the most practical for now. JPG for viewing and export. TIF/PNG/RAW for preservation and editing.

• Most image catalog software support JPG, PNG, TIF, and some other common formats. They usually do not support JPEG2000, JPEG-XR, EXR, HEIF, AVIF. Even formats commonly supported by web browsers, like WEBP, aren't supported by many programs.

  Picasa is a discontinued product, so if it's important to you, you're pretty much stuck with JPG.

• HDR support is not just about color depth, but also color representation. Most programs represent colors as sets of integers. For HDR, colors need to be represented in floating point to accommodate the vast difference between the brightest and darkest colors (dynamic range).

• Any format that compresses better than standard JPG is likely to take much longer to process.

Regarding some specific formats:

• JPEG2000 - Window of opportunity for mass adoption has passed. No tools to add and edit metadata.

• JPEG-XR - Not even Microsoft supports it anymore. (MS was the original developer.)

• JPEG XL - Currently in development. The standardization process has begun. IF it becomes widely adopted, it is a good candidate for your needs.

• HEIF - No tools to use high bit-depth colors. No tools to add and edit metadata. Support for format isn't great outside of Apple.

• AVIF - Still in development.

• EXR - Poor support in applications. Issues with linear vs logarithmic representation (colors may shift each time the file is opened and saved). Metadata?

• WEBP - Viewing is well supported by web browsers, but not image viewers. No tools to add and edit metadata.

• DNG - Not a general-purpose image format. Requires raw processing to produce an image for viewing and sharing.

You could roll your own image format, like BPG or FLIF. Then it would support whatever you want it to.