They know you overstayed and you have a one year ban starting from your departure date.
Yes it will affect your future reentry even after your ban is over. You will likely not get a UK visa for a very long time, maybe ever. Two years is a long time and immigration cannot trust you. They don’t care about your personal reasons.
You do not need to check with anyone, the rules are explicit
Voluntary departure at person’s own expense
Unless they are applying for entry clearance as a family member (under Appendix FM of the Immigration Rules), or they were under 18 at the time of their most recent breach (as set out at paragraphs A320 and 320(7B) of the Immigration Rules), the following categories of offender will ordinarily be subject to a mandatory one year re-entry ban if they leave the UK voluntarily at their own expense:
- illegal entrants
- those who breach a condition attached to their leave
those who overstay their lawful leave by more than:
o 90 days, excluding any exceptional periods, where the overstaying began up to and including the 5 April 2017
o 30 days, excluding any exceptional periods, where the overstaying began on or after 6 April 2017
If you married or somehow become a UK citizen or EU National, the overstay rules change