I'm willing to lay long odds 99+% of them are capturing to computer files. And 98+% in the cloud.

AI won't give a number, but seems to be lower, the best I could get was:

Based on the search results, it is not possible to make a precise estimate of the fraction of organizations that store incoming faxes digitally versus printing them by comparing the sales, capacity, and speed of fax machines and fax servers. However, the data reveals a strong trend toward digital adoption, which allows for an informed qualitative assessment.

Key findings from the search results indicate:

Digital Shift: The market for fax server software is growing rapidly, projected to reach $12.32 billion by 2030 with a CAGR of 12.75%. In contrast, the traditional fax machine market is either declining (CAGR of -5% projected) or growing very slowly (CAGR of 3.6%).
Cloud Dominance: Cloud-based fax solutions are the fastest-growing segment, accounting for 60% of the fax server software market share in 2023. These services inherently store faxes as digital files (e.g., PDFs in email or cloud storage).
Enterprise Adoption: A significant portion of enterprises are moving away from paper. One report states that around 38% of enterprises have already moved to digital fax infrastructure, and 42% are investing in hybrid cloud solutions, both of which prioritize digital storage.
Industry Drivers: Highly regulated industries like healthcare and finance are major drivers of this shift, as digital fax solutions provide the secure, auditable, and compliant document trails they require.