Let me turn this around:
When you're looking at some silly build like a single classed character, do you try to justify the class in-game, or do you prefer to ignore the fiction and concentrate on killing all the things?
I have never played in a world where the characters are aware that they have classes,what they are, and use them to define themselves and others. Trying to say that class - single or multi - is an in-game construct is patently false.
Now, every character interacts with the narrative, with what's going on. Some of these are free-form, non-mechanical interactions. Some of these are mechanical interactions within the system.
So if my character is brave, what class am I? No information, maaaaaybe we could assume you have a good Wisdom saving throw since that's how the system would support it when/if comes up. If my character can fire a bow well, what class am I? Well, that has some more mechanical expression so we can narrow to one of several classes. Or a combonation of them. Or perhaps them and something else because we haven't gotten a full read on the character. Is that archer woodsman with nature spells a ranger, or maybe a land druid / rogue (scout)? Or maybe a fighter / cleric (nature) with an appropriate background.
Singleclassing and multiclassing are just ways of picking the mechanical expression that best matches how your character interacts with the system part of the narrative. Multiclassing is a great tool when you aren't willing to limit your character vision to a set of pre-defined containers, instead mixing and matchng to better be able to represent in the narrative.
Be willing to play whatever is needed in order to realize the vision you have of your character, and that includes how they interact with the narrative. If you want to play a dashing swashbuckler, make them able to show themselves as both dashing and a swashbuckler - or any other combo. Don't let yourself be pidgeonholed, take the race, background and class(es) that best represent what you are trying to show.