When referring to a specific person by title only within a specific office, should the title be capitalized?

The Chicago Manual of Style, "8.22 Civil titles" says:

In formal prose, however, civil titles are capitalized only when used as part of the name (except as noted). See also 10.13.

By this, your sentence is rendered as:

XYZ University's board chairman and office manager shall provide the following documents by the September 1, 2021.

In "8.19 Titles and offices—the general rule," CMoS says

Civil, military, religious, and professional titles are capitalized when they immediately precede a personal name and are thus used as part of the name (traditionally replacing the title holder’s first name). In formal prose and other generic text, titles are normally lowercased when following a name or used in place of a name (but see 8.20)

Guidance in 8.20 says

In promotional or ceremonial contexts such as a displayed list of donors in the front matter of a book or a list of corporate officers in an annual report, titles are usually capitalized even when following a personal name. Exceptions may also be called for in other contexts for reasons of courtesy or diplomacy.

Maria Martinez, Director of International Sales

A title used alone, in place of a personal name, is capitalized only in such contexts as a toast or a formal introduction, or when used in direct address

Your sentence fits none of the cases mentioned.

However, were it in an annual report, you could arguably say

Severus Snape, XYZ University Board Chairman

Section 8.22 does wryly note:

Much of the usage below is contradicted by the official literature typically generated by political offices, where capitalization of a title in any position is the norm.

You're probably so used to seeing titles (needlessly) capitalized in press releases that it looks odd when they're not.