A few (4+) years ago, most offers were made without having to compete with another offer.  In such as a circumstance, it often made sense to tailor your preapproval letter to match the price you were offering.  For example...

$275,000 = List Price

$350,000 = Your Max Preapproval Amount

$265,000 = Your Offer

$265,000 = The Preapproval Letter You Include

After all, why let the seller know that you could pay $350K when you're trying to negotiate them down from $275K to $265K.  :-)

These days, however, things work a bit differently.  You should consider maximizing the amount of your preapproval letter to show your financial strength.

$350,000 = List Price

$475,000 = Your Max Preapproval Amount

$375,000 = Your Offer (after escalating)

$475,000 = The Preapproval Letter You Include

Yes, you could certainly include a preapproval letter from your lender showing you are qualified to pay $375K for the house -- but the strength of your finances will be much more evident to the sellers if you include the maximum preapproval letter of $475,000.

So... in a competitive offer scenario, don't hide the top price you can afford, as it might sway the seller in your favor as they are considering multiple offers.

Most sellers, if presented with these three offers would choose the third offer...

[1]  Offer of $375,000 with pre-approval letter of $375K

[2]  Offer of $375,000 with pre-approval letter of $395K

[3]  Offer of $375,000 with pre-approval letter of $475K

As a side note -- even if you don't want to spend $475K, and you won't spend $475K, if you qualify for $475K it can still be helpful to have that letter from your lender for the reasons outlined above.