Title is made up, from 'Sequence Index Digit Not'.

Challenge:

Given an integer n which is >= 0, output the n'th number of the following sequence.
Here are the first 50 items, with it's (0-indexed) index above it:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
1 0 3 2 5 4 7 6 9 8 22 20 30 24 23 26 25 28 27 32 11 33 10 14 13 16 15 18 17 31 12 29 19 21 50 40 41 42 44 45 35 36 37 51 38 39 52 53 55 56 34

How does this sequence work?

The number at index n must be the first in order that does not have any digits in common with n, and hasn't occurred yet for previous indexes. So when we look at normal sequence like this from 0-60:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

We define the n'th values like this:

• 0: The first number (0) contains the same digit, so we look for the next (1), which does not contain the same digit. So n=0 outputs 1.
• 1: The first number (0) does not contain the same digit, so n=1 outputs 0.
• 2: We've already encountered 0 and 1, and the next digit (2) contains the same digit, so we look for the next (3), which does not contain the same digit. So n=2 outputs 3.
• ...
• 10: We've already encountered 0-9, so the next in line is 10. 10-19 contain the matching digit 1, 20 contains the matching digit 0, 21 contains the matching digit 1 again, 22 is valid, so n=10 outputs 22.
• etc.

Challenge rules:

• If your language is 1-indexed (or you choose to) you are allowed to start the sequence at 3 2 5 4 7 ... (skipping the 1 at n=0 and the 0 at n=1).
• The minimum largest index you should support is 25,000. NOTE: The sequence stops at index 1,023,456,788, because the next index in line contains all 10 digits.
• You are also allowed to output / return an array/list of the entire sequence up to and including index n if you want to.

General rules:

• This is code-golf, so shortest answer in bytes wins.
  Don't let code-golf languages discourage you from posting answers with non-codegolfing languages. Try to come up with an as short as possible answer for 'any' programming language.
• Standard rules apply for your answer, so you are allowed to use STDIN/STDOUT, functions/method with the proper parameters and return-type, full programs. Your call.
• Default Loopholes are forbidden.
• If possible, please add a link with a test for your code.
• Also, please add an explanation if necessary.

Test cases:

This sequence actually created pairs regarding index and outputs. If index n outputs o, index o outputs n. So you can input either the left or right, and the output will be the other side:

0 <-> 1 (this test case is optional)
2 <-> 3
10 <-> 22
12 <-> 30
34 <-> 50
89 <-> 100
111 <-> 200
112 <-> 300
199 <-> 322
2231 <-> 4456
9605 <-> 11118
19235 <-> 46000
23451 <-> 60668
25000 <-> 13674

Here is a pastebin of the first 25,001 test cases if you want to try others.