On the subject of remote working being more productive or not, my anedoctal experience is that when remote working is fully embraced, the productivity skyrockets, but when it is embraced half-way it may have a negative effect.
When 2/3 of the employees are in an office, they tend to reach out to one another to discuss things and remote workers often get out of the loop. When everyone is working remotely, these discussions happen on slack channels for everyone to see. And if they are written down in a channel, folks can read it as many times as they need to ensure nothing was missed.
This may seem not to be too important, but it makes a massive difference at the end of the day. And you could try to make that happen without remote working but people will not stop walking out to someone else's cubicle for small questions when they have that option.