Does recursion in code still make my code linear to string length

Let's say I have two string s and t and I want to know if I can get from s to t via deleting, inserting or replacing a character in s. I have the following algorithm:

class Solution {
    public boolean isOneEditDistance(String s, String t) {
        return onedistance(s, t, 0, 0, 0);
    }
    
    private boolean onedistance(String s, String t, int si, int ti, int count) {
        
        if(count > 1) return false;
        while(si < s.length() || ti < t.length()) {
            if(si == s.length()) return onedistance(s, t, si, ti + 1, count + 1);
            if(ti == t.length()) return onedistance(s, t, si + 1, ti, count + 1);
            if(s.charAt(si) == t.charAt(ti)) {
                ti++;
                si++;
            } else {
                return onedistance(s, t, si + 1, ti, count + 1) || 
                    onedistance(s, t, si, ti + 1, count + 1) || 
                    onedistance(s, t, si + 1, ti + 1, count + 1);
            }
        }
        return count == 1;
    }
}

Basically, the idea is to keep track of current pointer si and ti for character we are comparing now for s and t, if they are the same move both pointer forward, else move either si or ti or both to represent adding, deleting or replacing a char in s, we can only do it once, so if count > 1 we return false, at the end we check if count is equal to one to know if edit distance between s and t is 1.

I am wondering now if my code is O(m + n) where m and n is length of s and t, because even we have the recursive part, we only do it once and return immediately if count > 1;