We have so many Feat options in PHB (and many more published since) for 5e, and yet many are notoriously underused. To address this, to also bring to the table more of the elements of space knight, spy agency, magic school, monastic mystery teachings and other fantasy training storytelling, please consider the following based on RAW (DMG pg 231 and various past faction and downtime-use elements):

The Savant faction is rooted in the traditions of renegades of an ancient and far flung Astral empire, whose peoples had ample time to devote themselves to pursuit of wondrous feats in the timeless void. They did not entirely forget their savage origins or history of combat, but sublimated their urges to greater achievements. Over time they evolved into practically a pure school of secret techniques of self-improvement, with their own mysterious goals of insurrection and liberty from a tyrant hardly any on the material worlds know or could conceive of. Savant Agents have restrictions placed on them to enhance their focus on training, and limited benefits from the Savant Academy other than constant, arduous exercise and study. Now, the study remains, cloistered and hidden, but few if any recall the original purpose of the Savant Academy.

Talent training is faction exclusive – feats from other sources still have downtime and cost requirements to advance in a talent in the Savant Academy. The Academy has to have income from some source, after all.

The learner must complete five talents of a lower level before advancing to study of any feat of the next level, and may not skip feats of lower level before taking on higher level feat training. For example, a Pupil with Defensive Duelist, Dual Wielder, Athlete, Tavern Brawler, Resilient (DEX), Crossbow Expert, Magic Initiate (Bard), Ritual Caster (Druid), Moderately Armored, and Heavily Armored may advance to the study of any of Sentinel, Grappler, Skulker, Warcaster or Medium Armor Master and can not yet study any feat of Kish or Ki level. Once an Apt learner in one Talent, there may be as many as four Talents the learner may still take up study of, starting at rank 1 (Ovate) in each of those Talents they wish to gain.

Each feat counts as one permanent magic item against a character’s magic item total. A character may still acquire magic items in the usual way, or through trade as normal, or by specific party, story or DM award. 

Training imposes in-game roleplay challenges for part of adventures at DM’s discretion, from speaking poorly-understood languages for linguist, or Actor communicating by only imitating sounds, to wearing an eyepatch for Keen Mind, Dungeon Delver, or Observant, to wearing non-proficient armor for Ironclad or exclusively using non-proficient weapons for Weapon Master or only preparing druid-accessible or Ritual Spells for Ritual Caster or using exclusively Bard-accessible spells for Magic Initiate, or taking encumbrance or exhaustion for Athlete or Durable, etc. The intention of this is to involve feat-learning as an aspect that affects characters more than just getting a neat in-game advantage others do not. It is not intended the DM make this too punitive a burden, however; make it fun.

Note that while this background incorporates specific race elements for flavor and favors wizards from races that grant light armor proficiency in some ways, any class/race combination can pursue such training so long as they qualify for each feat they wish to study. This will result in some characters who lack sufficiently high characteristics or who do not use their ASI to gain proficiency in light armor to be excluded from the highest achievements. That bias is intentional, as every game element has trade-offs.

In total 3,400 Downtime and gp cost, a year of playing four-hour sessions almost daily, averaging about two hundred Downtime and gp per level if someone wished to play a ninefold Ki – so a very slow advancement option – to complete all feats, or a  reason to continue adventuring past level 20 for a completionist. However, the real goal is to encourage the roleplay of an aspect of many fantasy characters' backgrounds, and to have fun while doing it.

Skill Proficiencies: This background provides only skill training through the rank 5 Scholar training, Skilled.

Savant Academy may teach skills to the learner's personal preference at such a high rank.

Tool Proficiencies: This background provides only tool training through the rank 5 Scholar training, Skilled.

Savant Academy tool training is most often in Smith's Tools or Thieves Tools, if tool proficiency is selected.

Languages: This background provides only languages through rank 2 Scholar training, Linguist.

Savant Academy linguists typically favor Draconic, Abyssal, Celestial, Infernal or Primordial.

Equipment: This background provides no equipment.

Suggested Characteristics

It is suggested that a character start with at least 11 in Charisma, and be of a class capable of casting spells.

Ability to wear at least light armor is preferred for learners.

The origins of the Savant Academy are Impious, so religious characters may find themselves at odds with their patrons or deities.

Lawful characters are favored by the Academy, but tyranny is strictly opposed by this Order.

Contacts

The Savant Academy trainer may appear as a special familiar, gotten in the ordinary way and other than being a demanding drill instructor is ordinary as a familiar of its type; or the trainer may appear as an NPC humanoid or series of NPCs, or some magical creature summoned by the Savant Academy with the mission of imposing training.