No there's no issues with OE spec Fazer batteries, Yes it's common for owners to forget to charge their bike over winter and it's very possible you've buggered yours, but all isn't lost.
All batteries discharge over time and this will accelerate if left connected to the bike, even if it's not switched on, current is being drawn from the battery, more so if you've got an alarm. Your typical alarm will flatten a good battery in 3 - 12 weeks depending on what type of alarm and temperature. If disconnected and stored in your home, it will last many months. If a battery is left to discharge too much, a standard rechange won't restore it, you'll need a special recovery programme charge, it's also possible even that can't save it. I won't get into cheap Chinese batteries, especially gel types
Most bike batteries/charging systems aren't (as standard) made to run accessories, also most charging systems aren't pumping out much below 5k. Which means the battery is supplying the power, if your battery isn't fully charged or has dead cells it's not going to last long. Heated grips are power hungry, some older types drawing up to 8 amps your 13 mile journey (one way) will be taking more out of the battery than the system can replace. Think of it like a tank of 10lts, you're taking out 2lt but only putting back 1lt per day it's not going to take long to run it empty/flat. Just testing the charging voltage wont tell you the battery is naff, just the charging system is working, similarly a voltage test across the battery won't tell you, cell are damaged, it will still show 12v plus if they are. You need a draw/load test, not easy if you've not go the kit and if done without it you could fry the battery.
Get yourself something like an optimate 3 or 4
https://optimate1.com/om3/ will do or higher if you want it to charge your car or Ctek charger
https://www.ctek.com/uk/products/car/mxs-3-8-uk this will charge all bikes and most cars. Both are around £50 ish, you can also buy an array of connections to suit your needs.
Both will run diagnostics, will run a recovery programme and tell you if your battery is buggered, both you can leave 24/7 or just top up once a month. If your battery is buggered don't buy cheap, about £45 upwards, yes you can get them for £25 or less but it's a gamble.