How I could add dir to $PATH in Makefile?

Did you try export directive of Make itself (assuming that you use GNU Make)?

export PATH := bin:$(PATH)

test all:
    x

Also, there is a bug in you example:

test all:
    PATH=bin:${PATH}
    @echo $(PATH)
    x

First, the value being echoed is an expansion of PATH variable performed by Make, not the shell. If it prints the expected value then, I guess, you've set PATH variable somewhere earlier in your Makefile, or in a shell that invoked Make. To prevent such behavior you should escape dollars:

test all:
    PATH=bin:$$PATH
    @echo $$PATH
    x

Second, in any case this won't work because Make executes each line of the recipe in a separate shell. This can be changed by writing the recipe in a single line:

test all:
    export PATH=bin:$$PATH; echo $$PATH; x

By design make parser executes lines in a separate shell invocations, that's why changing variable (e.g. PATH) in one line, the change may not be applied for the next lines (see this post).

One way to workaround this problem, is to convert multiple commands into a single line (separated by ;), or use One Shell special target (.ONESHELL, as of GNU Make 3.82).

Alternatively you can provide PATH variable at the time when shell is invoked. For example:

PATH  := $(PATH):$(PWD)/bin:/my/other/path
SHELL := env PATH=$(PATH) /bin/bash

What I usually do is supply the path to the executable explicitly:

EXE=./bin/
...
test all:
    $(EXE)x

I also use this technique to run non-native binaries under an emulator like QEMU if I'm cross compiling:

EXE = qemu-mips ./bin/

If make is using the sh shell, this should work:

test all:
    PATH=bin:$PATH x

Path changes appear to be persistent if you set the SHELL variable in your makefile first:

SHELL := /bin/bash
PATH := bin:$(PATH)

test all:
    x

I don't know if this is desired behavior or not.