At a campfire, distinguish effects triggered by entering the site from effects triggered by choosing Rest. That difference decides whether you can receive a relic’s benefit and still upgrade a card. The ordinary Rest versus Smith comparison changes when those effects are present.
Benefits from entering the site
Eternal Feather heals three HP for every five cards in your deck when you enter a rest site. With exactly 20 cards, that is 12 HP before choosing an action, subject to maximum health. Check the health bar after this recovery: the extra healing may allow Smith when you expected to need Rest.
Venerable Tea Set provides two extra energy at the start of the next combat after entering the site. Its trigger does not require choosing Rest. You can upgrade and still receive the opening energy. That can help a setup-heavy deck prepare for the next elite without giving up the desired card upgrade.
These benefits do not make every action equally useful. Extra opening energy still needs cards worth playing; Feather’s healing does not guarantee survival against the next enemy’s full sequence. Compare the resulting deck and HP with that encounter.
Benefits that require Rest
Stone Humidifier raises maximum HP by five whenever you Rest at a rest site. The decision therefore includes a lasting maximum-health gain, not only the immediate recovery. Choosing Smith does not activate that Rest trigger.
Regal Pillow adds 15 HP to the recovery from Rest. Read the resulting preview and your missing health. A large theoretical heal is partly wasted when there is little HP to restore; it is more useful when the route has already spent that health on difficult fights.
Pantograph is different again: its 25-HP heal occurs at the beginning of a boss combat. It can affect a campfire decision immediately before a boss, but it provides no recovery during ordinary fights between the campfire and that boss.
Extra actions compete for the same visit
Shovel allows digging for a random relic. Girya allows Strength gains at rest sites, with three uses maximum. Those options compete with the health or upgrade you would otherwise obtain. Their future benefit does not pay for an immediate defeat.
Miniature Tent changes this by allowing any number of rest-site options. Use the available combination instead of applying the ordinary single-action rule. It does not turn a Rest-triggered effect into an entry trigger: selecting the appropriate action still matters.
Before choosing, inspect your relics, the rest preview, the exact upgrade and the next forced fight. In route planning, value a campfire according to the actions and triggers your current run actually has, rather than treating every fire as the same reward.