I've worked at two fairly large companies during the pandemic, and both have publicly stated that their productivity has increased as a result of WFH. I've heard a variety of measures being mentioned such as profitability, hours worked per week, and responsiveness of employees when they are needed outside of normal working hours for production issues - they found people to be much easier to reach when their home office is their office.
It is clear, however that this data was gathered and released by a different part of the company than the ones that make the call on whether or not people will be required to come back in. Ultimately it's as we would expect: executive leadership deciding to pull people back in has little to do with data and more to do with feelings. Despite publishing that data and overwhelming support for full-time WFH, both have begun the process of pulling people back in.
>such as profitability, hours worked per week, and responsiveness of employees when they are needed outside of normal working hours for production issues
I'm sorry none of those are direct indication of productivity per se, even profitability, which is a long lagging indicator of productivity.
Anecdotally, we've seen more velocity in Jira from the same engineers - about 20% more. However, I've also noticed people are working more hours, which is more challenging to quantify. Hour-by-hour productivity may be a wash. Regardless, more stuff is getting done, and employee sentiment seems to remain the same as pre/post pandemic.
It's not an exact science, but based on our team's velocity which is tracked in Jira, we appear to complete more units of work while remote...but of course there are likely numerous factors to consider.