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Apache Guacamole might be a good option. "Clientless" (browser-based), supports various mfa, uses ssh/vnc/rdp on the backend.
However, if the data on that machine is sensitive, or if that machine has access to other sensitive things on your network, I'd suggest caution in allowing remote access from untrusted machines on the wider internet.
I'd recommend a full battery calibration before running the command one more time, if you haven't already (charge the battery fully, leave it on the charger at 100% for a while, then fully discharge until it shuts itself off, leave it for a bit, then fully recharge while off). If the calibrated values line up with a full:design ratio of ~80%, especially with a 10-year-old battery with almost 700 cycles on it, my take is that's pretty great.
That said, I think the best way to get an accurate feel for the health of an old battery is to put it through one full cycle of normal use and time how long it takes to die.