C (gcc), 96 71 bytes

Awesome -25 solution by ceilingcat

c;p;main(i){for(;read(0,&c,1);printf("%*c\n",i,p=c))c-p?:c-47?++i:--i;}

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Ungolfed

c; /* character */
p; /* previous character */

main(i /* indent */)
{
    for (; read(0, &c, 1); printf("%*c\n", i, p = c))
        c - p ? : c - 47 ? ++i : --i;
}

Explanation

read takes 1 byte from the file descriptor 0 (stdin) and stores it in c.

c - p checks if c and p are different. c - 47 checks if c is not a forward slash. So the entire conditional increments the indent if the character and the previous character are both backslashes, and decrements the indent if they're both forward slashes.

Then we print c with i leading spaces. We also assign p = c for the next iteration.

C (gcc), 96 71 70 bytes

Awesome -25 solution by ceilingcat

And another -1 by ceilingcat. ASCII bit hacks ftw

c;p;main(i){for(;read(0,&c,1);printf("%*c\n",i,p=c))c-p?:c&1?--i:++i;}

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Ungolfed

c; /* character */
p; /* previous character */

main(i /* indent */)
{
    for (; read(0, &c, 1); printf("%*c\n", i, p = c))
        c - p ? : c & 1 ? --i : ++i;
}

Explanation

read takes 1 byte from the file descriptor 0 (stdin) and stores it in c.

c - p checks if c and p are different. c & 1 checks if c is a forward slash. So the entire conditional increments the indent if the character and the previous character are both backslashes, and decrements the indent if they're both forward slashes.

Then we print c with i leading spaces. We also assign p = c for the next iteration.

C (gcc), 96 bytes

i;p;j;main(c){for(;~(c=getchar());printf("%c\n",p=c))for(j=c-p?i:c-47?++i:--i;j--;)printf(" ");}

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Ungolfed

i;
p;
j;

main(c)
{
    for (; ~(c = getchar()); printf("%c\n", p = c))
        for (j = c - p ? i : c - 47 ? ++i : --i; j--;)
            printf(" ");
}

Explanation

i (indentation), p (previous) and j (loop variable for printing spaces) are all integers initialised to 0

Get a character from stdin and store it in c (character). Break if it's EOF (-1)

If c and p are different, i stays the same. If c and p are the same, increment i if c is a backslash and decrement i if c is a forward slash

j = i

Print j spaces

 p = c

Print c and a newline

Get another character from stdin

C (gcc), 96 71 bytes

Awesome -25 solution by ceilingcat

c;p;main(i){for(;read(0,&c,1);printf("%*c\n",i,p=c))c-p?:c-47?++i:--i;}

Try it online!

Ungolfed

c; /* character */
p; /* previous character */

main(i /* indent */)
{
    for (; read(0, &c, 1); printf("%*c\n", i, p = c))
        c - p ? : c - 47 ? ++i : --i;
}

Explanation

read takes 1 byte from the file descriptor 0 (stdin) and stores it in c.

c - p checks if c and p are different. c - 47 checks if c is not a forward slash. So the entire conditional increments the indent if the character and the previous character are both backslashes, and decrements the indent if they're both forward slashes.

Then we print c with i leading spaces. We also assign p = c for the next iteration.

C (gcc), 96 bytes

i;p;j;main(c){for(;~(c=getchar());printf("%c\n",p=c))for(j=c-p?i:c-47?++i:--i;j--;)printf(" ");}

Try it online!

Ungolfed

i;
p;
j;

main(c)
{
    for (; ~(c = getchar()); printf("%c\n", p = c))
        for (j = c - p ? i : c - 47 ? ++i : --i; j--;)
            printf(" ");
}

Explanation

i (indentation), p (previous), j (loop variable for printing spaces) and c (character) are all integers initialised to 0

Get a character from stdin and store it in c. Break if it's EOF (-1)

If c and p are different, i stays the same. If c and p are the same, increment i if c is a backslash and decrement i if c is a forward slash

j = i

Print j spaces

p = c

Print c and a newline

Get another character from stdin

C (gcc), 96 bytes

i;p;j;main(c){for(;~(c=getchar());printf("%c\n",p=c))for(j=c-p?i:c-47?++i:--i;j--;)printf(" ");}

Try it online!

Ungolfed

i;
p;
j;

main(c)
{
    for (; ~(c = getchar()); printf("%c\n", p = c))
        for (j = c - p ? i : c - 47 ? ++i : --i; j--;)
            printf(" ");
}

Explanation

i (indentation), p (previous) and j (loop variable for printing spaces) are all integers initialised to 0

Get a character from stdin and store it in c (character). Break if it's EOF (-1)

If c and p are different, i stays the same. If c and p are the same, increment i if c is a backslash and decrement i if c is a forward slash

j = i

Print j spaces

p = c

Print c and a newline

Get another character from stdin