Background and Legacies
Outside the dungeons, pits, castles and sewers there is the chance to explore what the characters are more than just damage dealing machines, what they want to be their legacies, who they know, what they want to be; encourage players to expand on their backstories - or examine their backgrounds and see what can come out of the woodwork, not even as a battle but as someone to talk to or stories that they can find out about.
Relationships
High level characters should have not a small amount of fame and NPCs should be clamouring to apprentice/advise/woo/get money/kill them depending on what they've become famous for. Think Wizard duels to determine "the greatest magi of the land", building sage towers to tutor a school of magic, creating new religious movements, creating a guild of adventurers to solve all the petty tasks that no longer are worth the time, etc.
The world
At Epic level politics becomes an important factor; characters who are powerful can solve important problems, defeat enemies or swing wars between countries and Kings/Nobles/Wizards will want the PCs on their side - or rid of them - for wider political motives
Think scheming political figures "Have this castle as my thank you for your service" (said castle is crawling with dangerous bandits) religious orders that are asking for help with crusades and so on.
Making it alive
And those the players know will have moved on as well; NPCs shouldn't stand still, give a little snippet to important figures in the characters lives to make things feel more "alive", Bob and Bobette have had a baby, Duke Von Bob has created a new trade route, Trader Bob has partnered with his former enemy anti-Bob.
A world of shops and taverns?
Another thing to help the players feel a place is more alive is to add things to the city that are more than rumour-generation taverns and item-trading shops. Don't scattergun these in, you can drip feed them schools, colleges, magical research centres, masons guilds, graveyards and religious institutes to the point that (hopefully) they'll ask "is there an X" in town and then you can sit back and stuff in some generic NPCs for X, give it a name and have them talk to a piece of the city that they've effectively generated for you. Now that's lazy GM'ing and I like that :)
PC: "Is there an alchemist in the city?"
Me: (Checks list of random npc names, rolls a dice for personality on a quick chart), writes 'Alchemist, gruff, slightly mad, level 15' "Yes there is, a few inquiries tells you about Old Bob the Alchemists shop of chemical wonders, it's down old goat street."
No
As long as the break or tear is no larger than 1 foot in any dimension, you mend it (...)
You have stated that the tear in your cloak is longer than 1 foot, so you can't use Mending on it. It doesn't matter if the cloak itself fits within a 1 foot cube, since at least one of the tear's dimensions (its length) is larger than 1 foot, even if you fold it.
You might, however, want to try something like sewing it in the middle so that you have two smaller tears, and Mending it then, but only if your DM is prone to allow such shenanigans. Or just ask them directly if you could Mend your cloak, Mending does not usually influence the plot or gameplay in a major way, so he might just waive the constraints on it this time.
Best Answer
With the Work Downtime Activity, Up to Comfortable Lifestyle + 25 gp per week
This sounds a lot like the Work downtime activity from Xanathar’s Guide to Everything, and roughly the same type of activity as using tools, but substituting magic with the tools. By using this downtime activity, you can support earn enough to maintain a Poor to Comfortable Lifestyle for a given week, with exceptional rolls gaining an extra 25gp on top of the Comfortable Lifestyle. The amount you earn in a week depends on a skill check made to represent the type of work you do. A repair shop would typically be represented by the use of an Intelligence check + tool proficiency.
Now, since your spellcaster is not using tools, the above does not strictly apply. But given the similarities with the type of work being done, I would allow a check based on your spellcasting ability. Possibly include the proficiency bonus, similar to a spell attack roll and other similar spellcasting checks.
However, mending can generally only make small repairs. That means the range of services you can offer is smaller what you can do with regular old manual labor, and so one can expect a laborer whose talents are limited to this spell to have difficulty earning as much as someone that can use tools. Therfore, it may be reasonable to apply Disadvantage to the check. Unless you can come up with other magical supplements to your mending business.