To celebrate the White House’s newly renovated bowling alley, first lady Melania Trump hosted children of Secret Service members for an afternoon of strikes and gutters last week. “Be Best” branded shirts — a reference to her East Wing initiative — were hard to miss in the released photos. But the one thing missing from the happy images? Mrs. Trump’s face.

If a picture is worth a thousand words, then these photos were a near-perfect metaphor for Melania Trump’s time in “office.” The third Mrs. Trump is private and reserved, and seems to like it that way. The expertly crafted photos, ostensibly edited to protect the privacy of the minors, thoroughly encapsulate how Trump has defined the undefinable role of first lady thus far: She’s there. But, like, not really.

It’s not just a missed photo opportunity, say experts; it’s a complete miscalculation of the role. First ladies are the closest thing 1600 Pennsylvania Avenue has to an in-house celebrity. They are most often beloved, relatable and able to deploy charm offensives when politically necessary.

“The odd thing is it is so hard to get things done in American government. So you use every advantage that you possibly have,” says Lauren A. Wright, author of “On Behalf of the President: Presidential Spouses and White House Communications Strategy Today.” The public interest in Melania Trump is huge. When she wore a large brimmed white hat to greet visiting French President Emmanuel Macron, “Melania Trump hat” was Googled more than searches related to James Comey and his memos released the same week, says Wright, who was doing online research on the first lady at the time.

First ladies, Wright continues, can be an administration’s “single most valuable messaging tool.” And their programs “are typically used really strategically. There’s a lot of targeted intention behind it,” she points out. Former first lady Michelle Obama’s Let’s Move campaign represented a hard-to-argue-with olive branch of her husband’s Affordable Care Act. Laura Bush’s Ready to Read, Ready to Learn initiative had a direct correlation to her husband’s No Child Left Behind policy. Nancy Reagan’s Just Say No campaign was the softer side of President Reagan’s mandatory minimum sentence policy.

Be Best’s original three pillars — combating cyberbullying, promoting children’s social and emotional well-being, and fighting opioid abuse — don’t have cohesive messaging or a clear link to her husband’s policies, other than maybe the opioid element. On Tuesday, while celebrating the first anniversary of the program at the White House, Trump announced the expansion of the cyberbullying pillar to online safety for children. Yet the whole thing still seems nebulous.

First lady historian Katherine Jellison thinks Trump’s approach has been difficult to understand: “I think the jury’s still out on the current first lady. She’s sometimes very high-profile, but most of the times she’s not. She still is a mystery to me.” While Be Best was finding its footing, there were several aspects of Trump’s personal story that could have helped to smooth out her husband’s rough policy edges. Jellison points specifically to the Trump administration’s “America First” philosophy. She is an immigrant, speaks several languages and has worked abroad as a model. “She could have been deployed as the kinder, gentler face of America staying connected to the world as opposed to withdrawing from it,” Jellison notes.

One question that pops up around Trump is whether her arm’s-length handling of the first lady role is her own doing or a consequence of circumstance. The Trump administration has certainly seen its fair share of chaos and upheaval, which could be part of the explanation. But Jellison has another theory: Unlike past first ladies of the modern era, Trump did not have a hand in building her husband’s political career. “That was never a role she played and therefore may not be a role she’s comfortable with and even resists,” says Jellison.

At some point, explains Wright, every first lady comes face to face with the fact that she is, for better or worse, in the public eye. It appears that Trump, however, still hasn’t had this realization. “I don’t doubt she has amazing intention,” Wright says, “but I just don’t think she sees her role as strategic” — even though, as Wright puts it, the role of first lady “could not possibly be more important.”

Helena Andrews-Dyer is co-author of The Post’s Reliable Source column.