How to use the tr REPEAT modifier to replace a character with a repeated character?

I'm afraid you are misunderstanding the meaning of the "repeat" option.

tr, as you correctly infer, is used to translate character sets. You call it with option

tr set1 set2

The idea is that both sets can contain multiple characters, i.e. you can say

tr 'abc' 'def'

and it will replace every a with a d, every b with an e, and every c with an f. Now, sometimes you want to replace multiple "input" characters with the same "output" character, say

tr 'abcdefghij' 'xxxxxxxxyz'

This will replace a to h with x, i with y, and j with z. The "repeat" function is meant to make writing this less cumbersome, so that you can instead write

tr 'abcdefghij' '[x*8]yz'

as shorthand. Unfortunately, that means it is not designed for what you intend to do.

Instead, you can try sed

$ echo "1234" | sed 's/2/xxx/g'
1xxx34

This will substitute (s) all occurences (the trailing g) of 2 with xxx. Since sed is far more powerful than that (have a look at the questions tagged as sed for an overview of what is possible), it may be a good idea to have a look into anyway.