The developer uses MFA (TOTP, Push Notification, Yubikey etc) into a virtual desktop inside the organisation (Citrix, VMWare Horizon, etc).
From there, the developer can SSH / whatever into their development environment - which is hosted "inside" the corporate network, or their cloud provider, via internal links.
All code, and dev boxes live "inside" the corporate network, and only keypresses, mouse movement, and screen diffs are sent back and forth.
Most remote access packages can prevent clipboard, USB device, file transfer etc.
If you need a password manager for work purposes, then it lives on the corporate managed network - not your remote laptop/desktop - and to be really paranoid - you only ever "copy/paste" those passwords - you don't type them in.
If you really want to lock it down further, give the remote workers dedicated corporate equipment that they only use to access the remote desktops, so you can prevent some things like screen capturing, and really lock down the software to prevent things like keylogging software/malware.
You also should have the entire development environment segregated from the "business" corporate network as well.
It's only really an issue if you want to have offline developers - in which case I don't have any thoughts ready to hand - (but would expect it to be a very locked down machine, possibly with an even more locked down VM inside it).
As someone who regularly uses multiple layers of Virtual Desktop -> Virtual Desktop -> Remote Desktop, provided the network can handle it (on both your local network, and the corporate network), it works surprisingly well.