I thought of sex because:
she's inviting him to drink more and stay overnight at her house
she (seems to be) very clearly flirting
she emphasised them both being 'adults'
stopping by a shop immediately before staying the night is stereotypical 'picking up condoms' behaviour
the 'coward'...
the one question I always had during this manga was 'do condoms not exist in this universe?'
And even now I'm thinking 'do they know there are non-penetrative ways to show intimate sexual affection for each other?'
The whole story felt like it was looking for excuses to not explore those topics...
Note:
'happy New Year' = referring to the new year
'happy New Year's' = referring to the first day of the new year (shorthand for 'happy New Year's Day', so it requires an apostrophe)
'happy New Years' = incorrect, unless referring to multiple New Years