<think>
Okay, I need to implement the trim_caption function. Let's read the problem carefully.

The function should shorten a caption to a character budget. If the text is already within the limit, return it as is. Otherwise, return a shortened version ending with "…", which counts as one character. The process starts with the first limit-1 characters. But if the next character isn't a space and the kept part has a space, we need to drop back to the last space to avoid cutting a word in the middle. Also, if the first word is too long, just cut it short. Then, remove any hanging spaces before the ellipsis.

First, check if the input is a string and the limit is a positive integer. If not, raise a ValueError.

So, the first step is validation. If text is not a string or limit is not a positive integer, raise an error.

Next, if the length of the text is less than or equal to the limit, return it as is.

Otherwise, we need to process the text. The initial approach is to take the first limit-1 characters. But then check if the next character (at index limit-1) is not a space. If so, we need to find the last space before that position and truncate there.

Wait, the problem says: when the character just past the cut is not a space and the kept part holds a space, drop back to the last space. So, after taking the first limit-1 characters, check if the next character (limit-1) is not a space. If that's the case, then we need to find the last space in the first limit-1 characters and truncate there.

But also, if the first word is too long, just cut it short. So, if the first word is longer than the limit, we need to truncate it.

So, the steps are:

1. Check if text is a string and limit is a positive integer. If not, raise error.

2. If len(text) <= limit: return text.

3. Else:

   a. Take the first limit-1 characters.

   b. Check if the next character (limit-1) is not a space. If so, find the last space in the first limit-1 characters and truncate there.

   c. Also, check if the first word is longer than the limit. If so, truncate it.

But how to handle these steps?

Alternatively, the process is:

Start with the first limit-1 characters. Then, check if the next character (limit-1) is not a space. If that's the case, then we need to find the last space before that position and truncate there. But if there is no space, then we just take the first limit-1 characters and add the ellipsis.

But also, if the first word is longer than the limit, then we need to truncate it.

Wait, the problem says: a first word too long to fit is simply cut short. So, if the first word is longer than the limit, then we need to cut it to fit.

So, perhaps the approach is:

- Take the first limit-1 characters.

- Check if the next character (limit-1) is not a space. If so, find the last space in the first limit-1 characters and truncate there.

- Then, add the ellipsis.

But also, if the first word is longer than the limit, then we need to cut it.

Wait, maybe the steps are:

First, check if the text is longer than the limit. If so, process the text.

Take the first limit-1 characters. Then, check if the next character (limit-1) is not a space. If that's the