Luigi,
The Texas code states the following (TEXAS ENGINEERING AND LAND SURVEYING PRACTICE ACTS AND RULES CONCERNING PRACTICE AND LICENSURE):
§ 1001.401. USE OF SEAL.
(a) On receiving a license, a license holder shall obtain a seal in a design authorized by the board, showing the license holder’s name and the legend “Licensed Professional Engineer” or “Registered Professional Engineer.”
(b) [highlight #FCE94F]A plan, specification, plat, or report issued by a license holder for a project to be constructed or used in this state must include the license holder’s seal placed on the document.[/highlight] A license holder is not required to use a seal required by this section if the project is to be constructed or used in another state or country.
(c) A person may not place a seal on a document if the license of the license holder named on the seal has expired or has been suspended or revoked.
(d) A license holder is not required to use a seal under this section for a project for which the license holder is not required to hold a license under an exemption provided by Subchapter B.
(e) A license holder shall not be required to provide or hold any additional certification, other than a license issued under this chapter, to seal an engineering plan, specification, plat, or report.
In my experience working with Texas under an A/E, all generated drawings, specifications, calculations, datasheets, reports, etc. are stamped by a licensed individual. Where drawings were provided by other subcontractors, those drawings were stamped by the applicable originator, with the governing PE reviewing for acceptability to the project and final discipline stamp on the applicable package (this is only a seal that states are all required documents are present and is not on a drawing/spec, but a package coversheet with aforementioned statement.)
To answer your question on everything being stamped - This does not mean every nut and bolt needs a deliverable with a stamp, just those documents
generated by the engineer, or uniquely designed by the subcontractor. For example, details or the bounding criteria for equipment and components to be used can listed in the specifications, drawing schedule, or detail call-out and those documents stamped. We have not stamped commercial HVAC unit drawings from vendors, but our drawings we call them out on are, as they have been reviewed and selected by the engineer (or the spec detailing what size and type to get). If it was a unique one-of-a-kind, then yes, I would likely consider a stamp from the vendor.
In summary, everything generated by engineering has been stamped. I would imagine with a large facility that it would be broken into manageable groups with enough PEs to oversee the work. I highly recommend reviewing the contract requirements and reaching out to the board office for specific resolution.