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For now using formatted string literals (PEP498) is the fastest way of formatting strings.
$ ./python -m perf timeit -s 'k = "foo"; v = "bar"' -- '"%s = %r" % (k, v)'
Median +- std dev: 2.27 us +- 0.20 us
$ ./python -m perf timeit -s 'k = "foo"; v = "bar"' -- 'f"{k!s} = {v!r}"'
Median +- std dev: 1.09 us +- 0.08 us
The compiler could translate C-style formatting with literal format string to the equivalent formatted string literal. The code '%s = %r' % (k, v) could be translated to
 t1 = k; t2 = v; f'{t1!r} = {t2!s}'; del t1, t2
or even simpler if k and v are initialized local variables.
$ ./python -m perf timeit -s 'k = "foo"; v = "bar"' -- 't1 = k; t2 = v; f"{t1!s} = {t2!r}"; del t1, t2'
Median +- std dev: 1.22 us +- 0.05 us
This is not easy issue and needs first implementing the AST optimizer.

There isn't a direct mapping between %-formatting and __format__ format specifiers. Off the top of my head, I can think of at least one difference:
>>> '%i' % 3
'3'
>>> '{:i}'.format(3)
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
ValueError: Unknown format code 'i' for object of type 'int'
So you'll need to be careful with edge cases like this.
Also, for all usages of %s, remember to call str() (or add !s):
>>> '%s' % 1
'1'
>>> f'{1:s}'
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
ValueError: Unknown format code 's' for object of type 'int'
>>> f'{1!s:s}'
'1'
Although that also reminds me of this default alignment difference:
>>> x=0
>>> '%2s' % x
' 0'
>>> f'{x!s:2s}'
'0 '
>>> f'{x!s:>2s}'
' 0'
So, in general, the mapping will be difficult. On the other hand, if you can do it, and provide a function that maps between %-formatting codes and __format__ codes, then that might be a generally useful tool.

'%s' % x should be translated to f'{x!s}', not to f'{x:s}'. Only %s, %r and %a can be supported. Formatting with %i should left untranslated. Or maybe translate '%r: %i' % (a, x) to f'{a!r}: {"%i" % x}'.
It is possible also to introduce special opcodes that converts argument to exact int or float. Then '%06i' % x could be translated to f'{__exact_int__(x):06}'.

Serhiy, you actually did make a mistake above; `'%s' % x` cannot be rewritten as `f'{x!s}'`, only `'%s' % (x,)` can be optimized... 
(just try with `x = 1, 2`)

Thanks for the correction Antti. Yes, this is what I initially meant. This optimization is applicable only if the left argument of % is a literal string and the right argument is a tuple expression. Saying about `'%s' % x` I meant a component of the tuple.

PR 5012 implements transformation simple format strings containing only %s, %r and %a into f-strings.

I'm +1 on this optimization.

PR 26160 adds support of %d, %i, %u, %o, %x, %X, %f, %e, %g, %F, %E, %G.
What is not supported:
* Formatting with a single value not wrapped into a 1-tuple (like in "%d bytes" % size). The behavior is non-trivial, it needs checking whether the value is a tuple or a mapping. It would require adding more opcodes and AST nodes and generating complex bytecode.
* Mapping keys (like in "%(name)s"). They are rarely used, and if used, it is not performance critical.
* Precision for integer formatting. Precision is not supported in new-style formatting of integers, and it is not trivial to reproduce this behavior.
* Variable width and precision (like in "%*.*s"). It is possible to support them, but the code would be pretty complex, and the benefit is small, because this feature is rarely used and is not performance critical.
* Format code %c. It is relatively rarely used.
* Length modifiers "h", "l" and "L" (like in "%ld"). They ignored in Python and I did not see them in real code. While supporting them is easy, it would requires adding more than one line of code, it is not worth it.

commit a0bd9e9c11f5f52c7ddd19144c8230da016b53c6
Author: Serhiy Storchaka <storchaka@gmail.com>
Date: Sat May 8 22:33:10 2021 +0300
 bpo-28307: Convert simple C-style formatting with literal format into f-string. (GH-5012)
 
 C-style formatting with literal format containing only format codes
 %s, %r and %a (with optional width, precision and alignment)
 will be converted to an equivalent f-string expression.
 
 It can speed up formatting more than 2 times by eliminating
 runtime parsing of the format string and creating temporary tuple.
commit 8b010673185d36d13e69e5bf7d902a0b3fa63051
Author: Serhiy Storchaka <storchaka@gmail.com>
Date: Sun May 23 19:06:48 2021 +0300
 bpo-28307: Tests and fixes for optimization of C-style formatting (GH-26318)
 
 Fix errors:
 * "%10.s" should be equal to "%10.0s", not "%10s".
 * Tuples with starred expressions caused a SyntaxError.