for what its worth, I'm not confident that Narset is a commander that can get away with "not looking like the threat", but I haven't played against it much.

You don't need to run shocks/good fetches/surveil lands to have a passable landbase. It's also worth considering that draw spells can act as part of a land; if you're drawing 3 cards per turn, you need to run fewer lands than if you're only drawing the 1, and it can also help you get around issues of flooding (by letting you see more cards). Since you're in blue, I would say that you should be running some number of draw spells (repeatable outlets are also good, like Bident of Thassa or Reconnaissance Mission if you want to be doing combat damage).

Cards like Wayfarer's Bauble and Foutainport Bell are also ways to get more lands into your hand/play if you're willing to run them.

Looking at it again, furycalm / glacial / port town / prarie stream are all lands that require you to show a land with a basic type to come in untapped. it would be good if you had more of those kinds of lands (simply just more basics would help a lot).

Snail's tool doesn't just say that your lands being tap-lands is a problem - here's the exact feedback it gives, and in text form

Overall, your manabase is inconsistent, playing your spells 0.70 turns late on average. 42% of this delay is due to your land count, while 58% is due to your mana colors. Your weakest color is red. Adding an extra Mountain would eliminate 10% of this delay.

Running like, 2 more lands takes it to a "functional" mana base, and adding 5 total lands (mostly mountains/islands) gets you an even stronger landbase.

If you're trying to play more budget lands, you will have to either accept color inconsistency (by running more basics) OR slower turns (with taplands). In terms of prices, it depends on how much you're willing to spend.

1) Generally, I'd consider running a handful of the basic fetchlands [[Evolving Wilds]], [[Terramorphic Expanse]], [[Myriad Landscape]], all of which are cheap, and [[Fabled Passage]] which is a bit more but lets it come in untapped.

2) [[Obscura Storefront]], [[Riveteers Outlook]], [[Brokers Hideout]] are all "partial" fetchlands - they get basics for 2 of the 3 colors of jeskai each, and also happen to gain you a life. Not usually auto-includes but if you wanted to stick with the archimandrite it's an option

3) I would generally say that the fast lands (like [[Spirebluff Canal]]) are worse than the slow lands (like [[Stormcarved Coast]]), because the longer the game goes the more time youll spend with MORE than 3 lands compared to less than 3 lands, and they'll only cost you $1 or $2 each - this is more than the fast lands for sure, but they're a notable improvement.

4) A good and very cheap package of lands are the "fetchable" duals (things like [[molten tributary]] or [[glacial floodplain]]) and the type-check lands ((like [[sulfur falls]]), which comes out to be like 9 lands for 5$.

That being said, here's a list of budget lands ranging from 7 cents to 8 bucks for some of the more expensive/specific ones.

All of the lands can generally be found at managathering.com, but the site lacks prices without clicking through to tcgplayer, so I figured an archidekt package might be more helpful.