<think>
Okay, I need to implement the hex_groups function according to the given specifications. Let me start by understanding the requirements.

The function takes a list of byte values and a group width. Each byte should be converted to exactly two lowercase hexadecimal digits, zero-padded. Then, these bytes are grouped into chunks of the specified width. The groups are joined by single spaces. The last group might be shorter. If the input is invalid, like not a list, bytes out of range, or width not a positive integer, I need to raise a ValueError.

First, I need to validate the inputs. The values must be a list. Each element in the list must be an integer between 0 and 255. The width must be a positive integer. If any of these checks fail, raise ValueError with a short message.

Next, processing the bytes. For each byte, convert it to a two-digit hex string. Zero-padding is necessary, so using format specifiers like "{:02x}" would work. For example, 10 becomes "0a", 255 becomes "ff", and 3 becomes "03".

Once all bytes are converted to hex strings, they need to be grouped into chunks of the given width. For example, if the width is 2, the first two bytes form a group, then the next two, etc. The last group might have fewer elements if the total number isn't a multiple of the width.

So, I need to iterate over the list of hex strings in chunks of size 'width'. For each chunk, join the strings with no space (since each group is a sequence of hex strings concatenated), and then join all these groups with a single space between them.

Wait, the example given is hex_groups([10, 255, 3], 2) becomes "0aff 03". Let's see: the bytes are [10, 255, 3]. Each converted to two hex digits: 10 -> 0a, 255 -> ff, 3 -> 03. Then grouped into chunks of 2. The first group is [0a, ff], which becomes "0aff", and the second group is [03], which becomes "03". Then joined with a space: "0aff 03". So that's correct.

So the steps are:

1. Validate inputs.
2. Convert each byte to two hex digits.
3. Split the list into groups of 'width' elements.
4. Join each group into a string.
5. Join all group strings with a single space.

Now, for the code structure.

First, the function definition: def hex_groups(values: list, width: int) -> str.

Inside the function, first check if values is a list. If not, raise ValueError. Then check each element in values is an integer between 0 and 255. Also check that width is a positive integer.

Then, process each value in values to convert to hex. So, for each byte in values, format as two lowercase hex digits. So, for a byte in values, we can do f"{byte:02x}".

Once we have the list of hex strings, we need to split them into groups of 'width' elements. For example, if the list is [s0, s1, s2, s3, s4], and width is 2, the groups are [s0, s1], [s2, s3], [s4].

To split into chunks, I can use a loop that steps through the list in steps of 'width'. For i in range(0, len(hex_list), width),