My first implementation passed all tests, eventhough it evaluated
"1 + 2 * 3 * 4" to 28 (the correct answer is 25)

my bad, error was in my code
please remove/resolve this issue

Having a closer look at both the Random tests that pass and fail, I have a suspicion this is caused by the '/' symbol - which is shared by all three modes

I have failing tests when I attempt this in C# (in the Random and SymbolsEdge sets), which I can't explain.

For example, my solution fails on the following inputs:
"2>2 ZmU4sm7v.#56& e#M@ ¿ /+T," (Random test says: Expected value 216, my solution gives 214)
"Gk0_ @HN?/" (Random test says: Expected value 62, my solution gives 61)

I've tried the latter one manually, also arriving at 61. Here's the output:
from: (0, 0)
to: G (1, 1), mode: 2
takes: 1 shifts, totalling 6 presses
total: 6
from: (1, 1)
to: k (2, 0), mode: 1
takes: 2 shifts, totalling 9 presses
total: 15
from: (2, 0)
to: 0 (3, 7), mode: 1
takes: 0 shifts, totalling 3 presses
total: 18
from: (3, 7)
to: _ (4, 6), mode: 1
takes: 0 shifts, totalling 3 presses
total: 21
from: (4, 6)
to: (5, 1), mode: 1
takes: 0 shifts, totalling 5 presses
total: 26
from: (5, 1)
to: @ (3, 6), mode: 1
takes: 0 shifts, totalling 6 presses
total: 32
from: (3, 6)
to: H (1, 2), mode: 2
takes: 1 shifts, totalling 10 presses
total: 42
from: (1, 2)
to: N (2, 3), mode: 2
takes: 0 shifts, totalling 3 presses
total: 45
from: (2, 3)
to: ? (0, 2), mode: 3
takes: 1 shifts, totalling 11 presses
total: 56
from: (0, 2)
to: / (4, 8), mode: 3
takes: 0 shifts, totalling 5 presses
total: 61

I don't look ahead in the string to optimize for shift.

There's more to a Best Practice than asymptotic performance, e.g. readability and expressiveness.

Out of curiosity, what do you think the asymptotic performance of this solution is?

this solution would be hard to maintain if the requirements would change the number of lines in the field

this solution would be hard to maintain if the requirements would change the number of lines in the field or the character representing a pin