This anatomy site doesn't provide reputable citations, but I don't see any obvious inaccuracies and it has a reasonable section on potential clinical presentations of superficial fibular nerve injuries:
There are two relatively common pathologies involving the damage to the superficial fibular nerve; entrapment and direct damage (e.g from a comminuted fracture).
Superficial Fibular Nerve Entrapment
Superficial peroneal nerve entrapment (also known as nerve compression) can cause pain and paraesthesia over the lower leg and dorsum of the foot. Entrapment frequently results from ankle sprains or twisting of the ankle, as this causes the nerve to stretch in the lower leg.
Another cause of nerve entrapment occurs at the point where the nerve exits the deep fascia of the leg, the nerve becoming compressed by this fascia. Surgical decompression of the nerve therefore is used to provide relief from the symptoms and pain.
Direct Damage to the Superficial Fibular Nerve
The superficial fibular nerve may be damaged by fracture of the fibula, or by a perforating wound to the lateral side of the leg.
As the muscles that the superficial fibular nerve innervates are evertors, injury to the nerve may result in a loss of eversion. A loss of sensation over the majority of the dorsum of the foot and the anterolateral aspect of the lower leg could also result.
ScienceDirect provides summary pages with excerpts from relevant publications on many topics, including the fibularis muscles, which largely verifies the claims from the anatomy teaching site. I'll include two especially useful excerpts here.
Chapter 32 - Leg Injuries. Zetaruk & Hyman. Clinical Sports Medicine. 2007.
Athletes with compression of this nerve present with pain, numbness or paraesthesias in the distribution of the superficial peroneal nerve (i.e. anterolateral lower leg and dorsum of foot, including second to fourth toes) during exercise and occasionally at rest.
Clinical examination reveals decreased sensation most consistently over the dorsum of the foot after exercise. Tinel's sign over the site of the compression or pain with passive ankle flexion/supination may be elicited. Pressure over the site of entrapment while the patient actively plantarflexes and inverts the ankle may reproduce symptoms. A fascial defect may be detected on palpation.
Initial conservative treatment may include modification of aggravating activities and prevention of recurrent ankle inversions using bracing. Surgical decompression is the definitive treatment.
Chapter 19 - Compression and entrapment neuropathies. Bouche. Handbook of Clinical Neurology. 2013.
Superficial Fibular Neuropathy
Superficial fibular nerve compression or entrapment is unusual. Peroneal compartment syndrome is an uncommon disorder in which the muscle swelling and necrosis are limited to the fibular muscles. It can be due to excessive exercise, blunt trauma, or rupture of the peroneus longus. Fracture of the fibula may damage only the superficial fibular nerve...Causes were varied: muscle herniation, varicose veins, anterior and/or lateral compartment syndrome, anterior fasciotomy, or contusion. There was decreased sensation and pain over the dorsum of the foot at rest or during exercise. Reduced nerve conduction velocity of the superficial fibular nerve below 44 m/s was considered abnormal.
You'll notice that these articles make little mention of motor defects, including your hypothesized "constant supination of the foot," like those motor deficiencies that occur with comparable brachial plexus injuries. This is because the eversion action of the muscles supplied by the superficial fibular nerve is supplemented by muscles innervated by the deep (profundus) fibular nerve (whereas brachial plexus injuries "knock out" entire muscle groups that work in opposition to a still-active group).
With superficial fibular nerve pathologies, the supinating action of the muscles supplied by n. fibularis profundus isn't so strongly unopposed that a remarkable club foot presentation appears, but long-term superficial peroneal nerve dysfunction still limits function in the lower leg and can be treated non-invasively:
Evaluation and treatment of peroneal neuropathy. Baima & Krivickas. Curr Rev Musculoskelet Med. 2008.
If the patient has isolated superficial peroneal nerve palsy, he may benefit from a shoe insert with a lateral wedge to prevent supination of the foot from weakness of the evertors.